info@viam.science.tsu.ge (+995 32) 2 30 30 40 (+995 32) 2 18 66 45

Tamaz Tadumadze

  • Differential Equations and Optimal Control Department
    Head / Chief Researcher
  • Office: room 256, University str.11, 0186 Tbilisi, Georgia
  • Phone: 593 61 23 74
  • E-mail: tamaz.tadumadze@tsu.ge
  • Research fields: Optimal Control of Functional Differential Equations (Necessary Conditions, Existence Theorems, Regu

Summary

Education:
1996 - scientific-pedagogical rank of professor (TSU)
1985 - Ph.D., Razmadze Institute of Mathematics of the Georgian Academy of Sciences
1975 - equivalent to a doctor, candidate of physics and mathematics sciences, Iv. Javakhishvili Tbilisi State University
1970-1973 - Aspirant from Iv. Javakhishvili Tbilisi State University
1965-1970 – Iv. Javakhishvili Tbilisi State University, Student of Faculty of Mechanics and Mathematics

Work Experience:
2012 – present Senior researcher at the I. Vekua Institute of Applied Mathematics of TSU
2017-present TSU, I. Head of the Department of Differential Equations and Optimal Control at the I. Vekua Institute of Applied Mathematics
2006- present Iv. Javakhishvili Tbilisi State University, Department of the Faculty of Exact and Natural Sciences, Professor; Head of the Department of Differential Equations;
1992 – 2005 TSU, professor of the Control Theory department
1993 – 2006 Head of the department of the Vekua Institute of Applied Mathematics of TSU
1986 - 1992 Chief scientific researcher of the Vekua Institute of Applied Mathematics of TSU
1978 - 1985 Senior researcher at the Vekua Institute of Applied Mathematics of TSU
1973 - 1977 Junior researcher at the Vekua Institute of Applied Mathematics of TSU

Additional Information
The author of more than 150 articles including 6 monographs; Supervisor of 9 Doctoral
Dissertations. Under his supervisor, many masters and bachelor's works, student projects have
been prepared. Tea Shavadze's projects, under his leadership, won the following grants: Grant
for the Young Scientists of the Shota Rustaveli National Science Foundation; Grant for the
Doctoral Education Programs of the Shota Rustaveli National Foundation.
Participated in many scientific forums, including: Symposium on Differential Equations and
Mathematical Physics, December 24-25, 2003, Tbilisi, Georgia. The International Conference
,,Problems of Cybernetics and Informatics”, October 24-26, 2006, Baku, Azerbaijan. Fourth
International Conference on Applied Mathematics and Computing, August 12-18, 2007, Plovdiv,
Bulgaria. The 2nd International Conference on Control and Optimization with Industrial
Applications, June 2-4, 2008, Baku, Azerbaijan. Workshop „Problemes Inverses, Controle de
Bord et Applications”, December 17-18, 2008, Nantes, France. International Congress of
Mathematicians, August 19-27, 2010, Hyderabad, India. Second International Conference
Mathematics in Armenia: Advances and Perspectives, August 24-31, 2013, Tsaghkadzor,

Armenia. Conference on Functional Differential Equations and Applications-FDEA, August 24-
29, 2014, Ariel, Israel. First Salerno-Tbilisi Workshop on Modeling in Mathematics, February
24-26, 2014, Salerno, Italy. Swedish-Georgian Conference in Analysis and Dynamical
Systems, July 15-22, 2015, Tbilisi, Georgia. 11th International Conference Numerical Analysis
and Optimization Days-Jano11’, April 27 -29, 2016, Beni Mellal, Morocco. 8 th Israel-Czech
Workshop On "Functional Differential Equations", August 27, 2017, Ariel University, Ariel,
Israel. The International Workshop on the Qualitative Theory of Differential Equations,
December 18-20, 2021, Tbilisi, Georgia. XXXVI International Enlarged Sessions of the Seminar
of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, April
19-21, 2022 Tbilisi, Georgia.
Teaching Courses: Ordinary Differential Equations; Elected Questions of Ordinary Differential
Equations; Functional Differential Equations; Optimal Control of Functional Differential
Equations; Some Questions of Variation Analysis.
Awards: A. Razmadze Award of the Georgian National Academy of Sciences-2001; The
Order of Honor-2013; I. Javakhishvili Medal of TSU.

Projects

Talks

  • Representation formulas of the First Variation of Solution for One Class of Neutral Functional-Differential Equation with the Continuous and Discontinuous Initial Conditions, by Tea Shavadze (Speaker), Tamaz Tadumadze at Global Conference on Education (GCEDU), 2023, Dubai, UAE.
  • On the Representation of a Solution for the Perturbed Quasi- Linear Controlled Neutral Functional Differential Equation, by Tea Shavadze (Speaker), Tamaz Tadumadze at 17th Annual International Conference on Mathematics: Teaching, Theory & Applications, 2023, Athens, Greece.
  • On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral Functional-Differential Equation, by Tea Shavadze (Speaker), Tamaz Tadumadze at The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), 2023, Tbilisi, Georgia.
  • Mathematics at the Ivane Javakhishvili Tbilisi State University., by Omar Purtukhia (Speaker), Tamaz Tadumadze at The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), 2023, Tbilisi, Georgia.
  • On the Optimization Problem of One Market Relation Containing the delay Functional Differential Equation, by Tamaz Tadumadze (Speaker), Phridon Dvalishvili, Abdeljalil Nachaoui, Mourad Nachaoui at The International Workshop on the Qualitative Theory of Differential Equations, 2023, Tbilisi, Georgia.
  • SENSITIVITY COEFFICIENTS OF A CONTROLLED FUNCTIONALDIFFERENTIAL MODEL OF THE IMMUNE RESPONSE CONSIDERING OF THE MIXED INITIAL CONDITION AND VARIATION OF THE INITIAL MOMENT, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui, Mourad Nachaoui at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, 2023, Tbilisi, Georgia.
  • International Workshop on the Qualitative Theory of Differential Equations, by Tamaz Tadumadze (Speaker) at International Workshop on the Qualitative Theory of Differential Equations, 2021, Tbilisi, Georgia.
  • On the Representation of a Solution for the Perturbed Controlled Differential Equation with the Discontinuous Initial Condition Considering Perturbation of the Initial Moment, by Tea Shavadze (Speaker), Tamaz Tadumadze at International Workshop QUALITDE – 2021, December 18 – 20, 2021, Tbilisi, Georgia , 2021, Tbilisi, Georgia.
  • Existence theorems of an optimal element for the two-stage variational and optimal problems with discrete delays, by Tamaz Tadumadze (Speaker) at XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, 2020, Tbilisi, Georgia.
  • The Equation in Variations for the Controlled Differential Equation with Delay and its Application, by Tamaz Tadumadze (Speaker), Tea Shavadze, Abdeljalil Nachaoui at International Workshop on the Qualitative Theory of Differential Equations, 2019, Tbilisi, Georgia.
  • Delay Optimization Problem for One Class of Functional Differential Equation, by Tea Shavadze (Speaker), Tamaz Tadumadze, Medea Iordanishvili at Functional Differential Equations and Applications FDEA 2019, 2019, Ariel, Israel.
  • On one inverse problem for the linear controlled neutral differential equation, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui, Fatima Aboud at International Workshop on the Qualitative Theory of Differential Equations, 2018, Tbilisi, Georgia.
  • Sensitivity analysis of delay differential equations and optimization problems, by Tamaz Tadumadze (Speaker) at 6th International Conference on Control and Optimization with Industrial Applications, 2018, Baku, Azerbaijan.
  • Some questions of the qualitative theory of functional differential equations with several delays : variation formulas of solutions, optimization , inverse problems, by Tamaz Tadumadze (Speaker) at 6 th Ariel University Conference on “Functional Differential Equations and Applications, 2017, Ariel, Israel.
  • Some questions of the qualitative theory of delay differential equations: variation formulas of solutions, optimization, sensitivity analysis, by Tamaz Tadumadze (Speaker), Phridon Dvalishvili at International scientific conference on “ Theoretical and Applied problems of Mathematics”, 2017, Sumgayit, Azerbaijan.
  • Effects of Several Delays Perturbations in the Variation Formulas of Solution of a Functional Differential Equation with the Discontinuous Initial Condition, by Tamaz Tadumadze (Speaker) at International Workshop on the Qualitative theory of Differential Equations, 2016, Tbilisi, Georgia.
  • Variation formulas of solution and initial data optimization problem for delay functional differential equations with the discontinuous initial condition, by Tamaz Tadumadze (Speaker) at The 11 th International Conference of Numerical Analysis and Optimization , Days JANO’11, 2016, Beni - Mellal, Morocco.
  • On the Representations of Sensitivity Coefficients for Nonlinear Delay Functional Differential Equations with the Discontinuous Initial Condition, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui at International Workshop on the Qualitative Theory of Differential Equations, 2015, Tbilisi, Georgia.
  • Sensitivity analyses for some classes of controlled dynamical systems with time-delay, by Tamaz Tadumadze (Speaker) at Swedish-Georgian conference in analyses and dynamical system, 2015, Tbilisi, Georgia.
  • Variation formulas of solution for a neutral functional- differential equation taking into account delay function perturbation and the discontinuous initial condition, by Tamaz Tadumadze (Speaker), Nika Gorgodze at Conference on Functional Differential Equations and Applications (FDEA 2014), 2014, Ariel, Israel.
  • Sensitivity analysis of one class of controlled functional differential equation considering variable delay perturbation and the continuous initial condition, by Tamaz Tadumadze (Speaker) at International Workshop on the Qualitative Theory of Differential Equations, 2014, Tbilisi, Georgia.
  • Initial data optimization problems for one class of neutral functional differential equation with the continuous initial condition, by Tamaz Tadumadze (Speaker), Nika Gorgodze at International Workshop on the Qualitative Theory of Differential Equations "QUALITDE – 2013", 2013, Tbilisi, Georgia.
  • Variation formulas of solution for differential equations taking into account delay function perturbation and initial data optimization problems, by Tamaz Tadumadze (Speaker), Nika Gorgodze at Second International Conference Mathematics in Armenia : Advances and Perspectives, 2013, Tsaghkadzor, Armenia.
  • On the well-posedness of the Cauchy problem for a functional differential equation taking into account variable delay perturbations, by Tamaz Tadumadze (Speaker) at The International Conference Lie Groups, Differential Equations and Geometry, 2013, Batumi, Georgia.
  • On the existence of an optimal initial element for neutral functional differential equations, by Tamaz Tadumadze (Speaker) at International Conference ,, Functional Differential Equations 2012”, 2012, Ariel, Israel.
  • Optimization of initial data for nonlinear delay functional-differential equations with the mixed initial condition, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui, Nika Gorgodze at The International Workshop on the Qualitative Theory of Differential Equations, 2011, Tbilisi, Georgia.
  • On new effects of constant delays in variation formulas and optimality conditions, by Tamaz Tadumadze (Speaker) at The IV Congress of the Turkic World Mathematical Society, 2011, Baku, Azerbaijan.
  • On new effects of constant delays in variation formulas and optimality conditions, by Tamaz Tadumadze (Speaker) at The IV Congress of the Turkic World Mathematical Society, 2011, Baku, Azerbaijan.
  • On the optimization of initial data for delay differential equations, by Tamaz Tadumadze (Speaker) at The Third International Conference ,, Problems of Cybernetics and Informatics”, 2010, Baku, Azerbaijan.
  • On the optimality of an initial data for delay differential equations, by Tamaz Tadumadze (Speaker) at The International Congress of Mathematicians, 2010, Hyderabad, India.
  • Existence of optimal initial data for a quasi-linear neutral differential equation, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui, Akaki Arsenashvili at Fifth Congress of Mathematicians of Georgia, 2009, Batumi/Kutaisi, Georgia.
  • Optimal control and inverse problems for some classes of neutral differential equations, by Tamaz Tadumadze (Speaker), Abdeljalil Nachaoui, Akaki Arsenashvili at “Problemes Inverses , controle de bord et applications”, 2008, Nantes, France.
  • An inverse problem for some classes linear functional differential equations, by Tamaz Tadumadze (Speaker) at The 2 nd International Conference on Control and Optimization with Industrial Applications, 2008, Baku, Azerbaijan.
  • Formulas of variation of solution for variable structure delay differential equation with mixed intermediate condition and their applications in optimal problems, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at International Conference on Modern Problems in Applied Mathematics, 2008, Tbilisi, Georgia.
  • Optimization of delay controlled systems with non-fixed initial moment nd mixed initial condition, by Tamaz Tadumadze (Speaker) at International Conference on Modern Problems in Applied Mathematics, 2008, Tbilisi, Georgia.
  • Title-Optimization of delay variable structure control systems with mixed intermediate condition, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at Symposium on Contemporary Mathematics and its Applications, 2007, Batumi, Georgia.
  • Optimization of delay dynamical systems with mixed initial condition, by Tamaz Tadumadze (Speaker), Guram Kharatishvili at Symposium on Contemporary Mathematics and its Applications, 2007, Batumi, Georgia.
  • Optimization of delay control systems with non-fixed initial moment, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at The Fourth International Conference of Applied Mathematics and Computing, 2007, Bulgaria, Plovdiv.
  • Formula of variation for solution of neutral differential equation with distributed delay in controls and its applications to optimal control problems, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili, Nika Gorgodze, Ia Ramishvili at The International Conference ,, Problems of Cybernetics and Informatics”, 2006, Baku, Azerbaijan.
  • Optimal control of delayed variable structure systems with discontinuous initial condition, by Tamaz Tadumadze (Speaker), Akaki Arsenashvili at The st1 International Conference on Control and Optimization with Industrial Applications, 2005, Baku, Azerbaijan.
  • Formulas of variation of solution for quasi-linear controlled neutral differential equations with discontinuous and continuous initial conditions, by Tamaz Tadumadze (Speaker), Ia Ramishvili at Symposium on Differential Equations and Mathematical Physics, 2003, Tbilisi, Georgia.
  • Delay Dynamic Mathematical Model of Output of the Production and Optimal Control Problem, by Tamaz Tadumadze (Speaker), Guram Kharatishvili at SCI 2002 in Tbilisi “Control Systems”-Invited Session(IS00461) ( Under the framework of The 6 th World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida, July 14-18, http:www, 2002, Tbilisi, Georgia.

Publications

  • Abdeljalil Nachaoui, Tea Shavadze, Tamaz Tadumadze, On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition, Georgian Math. J. 2024, De Gruyter , 2024.
  • Medea Iordanishvili, Tea Shavadze, Tamaz Tadumadze, Necessary Optimality Conditions of Delay Parameters for the Nonlinear Optimization Problem with the Mixed Initial Condition., Commun. Optim. Theory 2023 (2023) 2, Mathematical Research Press, London, UK, 2023.
  • Tea Shavadze, Tamaz Tadumadze, On the Well-Possednis of the Cauchy Problem for a Neutral Controlled Functional Differential Equation, Functional Differential Equations, 29 (3- 4), 2023, Israel, Ariel University Press, 2023.
  • Phridon Dvalishvili, Abdeljalil Nachaoui, Mourad Nachaoui, Tamaz Tadumadze, On the Optimization Problem of One Market Relation Containing the delay Functional Differential Equation, Reports of Qualitde-2023, Volume 2, 2023, Tbilisi State University Press, 2023.
  • Abdeljalil Nachaoui, Mourad Nachaoui, Tamaz Tadumadze, Meshless Methods to Noninvasively Calculate Neurocortical Potentials from Potentials Measured at the Scalp Surface, New Trends of Mathematical Inverse Problems and Applications,Springer Proceedings in Mathematics & Statistics 428 (2023), Springer Nature Switzerland AG 2023, 2023.
  • Tea Shavadze, Tamaz Tadumadze, EXISTENCE OF AN OPTIMAL ELEMENT FOR A CLASS OF NEUTRAL OPTIMAL PROBLEMS, Mem. Differential Equations Math. Phys. 86 (2022), pp. 127-138., Tbilisi University Press , 2022.
  • Abdeljalil Nachaoui, Tamaz Tadumadze, ON THE NUMERICAL APPROXIMATION OF SOME INVERSE PROBLEMS GOVERNED BY NONLINEAR DELAY DIFFERENTIAL EQUATION, RAIRO-Oper. Res. 56 (2022) 1553–1569, Recherche opérationnelle, 2022.
  • Tea Shavadze, Tamaz Tadumadze, Abdeljalil Nachaoui, On the Coefficient of Sensitivity of a Controlled Differential Model of the Immune Response, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Tbilisi State University Press, 2022.
  • Ia Ramishvili, Tea Shavadze, Tamaz Tadumadze, A Controlled Integral Equation and Properties of its Kernel, Bulletin of TICMI, 26(2), pp. 81–88, 2022, Tbilisi State University Press, 2022.
  • Tamaz Tadumadze, Lela Alkhazishvili, Medea Iordanishvili, A delay optimization problem for the linear control system with the mixed initial condition, Sem. I. Vekua Inst. Appl. Math., Rep. 47, 3- 11, Tbilisi University Press, 2021.
  • Tea Shavadze, Tamaz Tadumadze, On the Representation of a Solution for the Perturbed Controlled Differential Equation with the Discontinuous Initial Condition Considering Perturbation of the Initial Moment, Abstracts of the International Workshop on the Qualitative Theory of Differential Equations, December 18-20, Tbilisi , Georgia ,181-184, www. rmi. ge/eng/ QUALITDE-2021/workshop_ 2021. htm, 2021.
  • Medea Iordanishvili, Tea Shavadze, Tamaz Tadumadze, Delay optimization problem for one class of controlled functional differential equation, Functional Differential Equations, 26 (3-4), 185-191, Ariel University Center of Samaria, 2020.
  • Abdeljalili Nachaoui, Tea Shavadze, Tamaz Tadumadze, The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition, Mathematics. 2020; 8(10):1845. https://doi.org/10.3390/math8101845, MDPI Proceedings Journals, Switzerland, 2020.
  • Phridon Dvalishvili, Tamaz Tadumadze, Abdeljalili Nachaoui, Effects of the initial moment and several delays perturbations in the variation formulas of a solution of a functional differential equation with the continuous initial condition, Georgian Math. J., V. 27, 1, 53–66, De Gruyter, 2020.
  • Tamaz Tadumadze, On the existence of an optimal element for one class of a two-stage optimal problem with phase restrictions, Semin. I. Vekua Inst. Appl. Math., Rep., 46, Tbilisi University Press, 2020.
  • Tamaz Tadumadze, Phridon Dvalishvili, Tea Shavadze, On the Representation of Solution of the Perturbed Controlled Differential Equation with Delay and Continuous Initial Condition, Appl. Comput. Math. 18 (3), 305-315, Institute of Applied Mathematics of Baku State University, 2019.
  • Tamaz Tadumadze, Tea Shavadze, Abdeljalili Nachaoui, The Equation in Variations for the Controlled Differential Equation with Delay and its Application, Abstracts of the International Workshop on the Qualitative Theory of Differential Equations, December 07-09, 2019, Tbilisi, Georgia,, http://www.rmi.ge/eng/QUALITDE-2019/workshop_2019.htm, 2019.
  • Tamaz Tadumadze, Tea Shavadze, VARIATION FORMULAS OF SOLUTIONS FOR THE CONTROLLED FUNCTIONAL DIFFERENTIAL EQUATIONS CONSIDERING DELAY PARAMETERS PERTURBATIONS AND OPTIMAL CONTROL PROBLEMS, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Vol. 45, 2019, I. Vekua Institute of Applied Mathematics, 2019.
  • Medea Iordanishvili, Tea Shavadze, Tamaz Tadumadze, Delay Optimization Problem for One Class of Functional Differential Equation, Springer Proceedings in Mathematics & Statistics. pp. 177-186, Springer, 2019.
  • Tamaz Tadumadze, Phridon Dvalishvili, Optimization of one marketing relation model with delay, Journal of Modern Technology and Engineering, 4, No.1, 5-10, Jomard Publisher, 2019.
  • Tamaz Tadumadze, Variation formulas of solution for a class of controlled differential equation with delay in the phase coordinates and controls, Advanced Mathematical Models and Applications, 3(1) , 30-38, Jomard Publisher, 2018.
  • Tamaz Tadumadze, Abdeljalili Nachaoui, Title-On One Inverse Problem for the Linear Controlled Neutral Differential Equation, International Workshop on the Qualitative Theory of Differential Equations QUALITDE-2018, 01-03 December, 2018, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia, 183-186, http://www.rmi.ge/eng/QUALITDE-2018/workshop_2018.htm, 2018.
  • Tamaz Tadumadze, Sensitivity analysis of delay differential equations and optimization problems, Proceedings of the 6 th International Conference on Control and Optimization with Industrial Applications, Volume I, 11-13 July, 367- 369, Baku State University, 2018.
  • Phridon Dvalishvili, Tamaz Tadumadze, Abdeljalili Nachaoui, Theorems on the continuous dependence of the solution on perturbations of the initial data and the right-hand side of equation are proved. Under initial data we understand the collection of initial mo, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 43, (1), 146-160, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2017.
  • Tamaz Tadumadze, Variation formulas of solutions for functional differential equations with several constant delays and their applications in optimal control problem, Mem. Differential Equations Math. Phys. 70 , 7-97, Tbilisi University Press, 2017.
  • Tamaz Tadumadze, On the well-posedness of the Cauchy problem for a neutral differential equation with distributed prehistory, Bulletin of TICMI , 21 (1), 3-8, Tbilisi University Press, 2017.
  • Tamaz Tadumadze, Phridon Dvalishvili, Continuous dependence of the minimum of functional on perturbations in optimal control problems with distributed and concentrated delays, Differential and Difference Equations with Applications, ICDDEA, Amadora, Portugal, May 2015, Selected Contributions, Springer Proceedings in Mathematics & Statistics, 164 ,339-348, Springer International Publishing Switzerland, 2016.
  • Nika Gorgodze, Tamaz Tadumadze, Ia Ramishvili, Continuous dependence of solution of a neutral functional differential equation on the right-hand side and initial data considering perturbations of variable delays, Georgian Math. J., 23 (4) , 519-535, De Gruyter, 2016.
  • Phridon Dvalishvili, Nika Gorgodze, Tamaz Tadumadze, Variation formulas of solution for neutral functional-differential equations with regard for the delay function perturbation and the continuous initial condition, Mem.Differential Equations Math.Phys. 64(2015), 163-168, Tbilisi University Press, 2015.
  • Tamaz Tadumadze, Inverse problem about transition in a fixed point for linear neutral neutral functional differential equations, Semin. I. Vekua Inst. Appl. Math., Rep., 41 , 59-62, Tbilisi University Press, 2015.
  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of a solution and initial data optimization problems for quasi-linear neutral functional differential equations with discontinuous initial condition, Mem.Differential Equations Math.Phys. 63, 1-77, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a class of controlled neutral functional- differential equations considering delay function perturbation and the continuous initial condition, Sem. I. Vekua Inst. Appl. Math., Rep. 40(2014), 45-49, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Abdeljalili Nachaoui, On the existence of an optimal element in quasi-linear neutral optimal problem, Sem. I. Vekua Inst. Appl. Math., Rep., 40, 50-67, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Conntinuous dependence of solutions of delay functional differential equations on the right-hand side and initial data considering delay perturbations, Georgin International Journal of Science and Technology, V. 6, No. 4 , 353-369, Nova Science Publishers, Inc., 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a neutral functional-differential equation taking into account delay function perturbation and the discontinuous initial condition, Functional Differential Equations, V. 21, No. 3-4 , 147-154, Ariel University Center of Samaria, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Initial data optimization problem for the quasi-linear neutral functional differential equation with variable delays and the discontinuous initial condition, Proceedings of I. Vekua Institute of Applied Mathematics, 64 , 68-73, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation Formulas of Solution for a Functional Differential Equation with Delay Function Perturbation, Journal of Contemporary Mathematical Analysis , 49 (2), 53- 63, Springer, 2014.
  • Tamaz Tadumadze, Variation formulas for solution of delay differential equations with mixed initial condition and delay perturbation, Nonlinear Oscillations, V. 17, No. 4, 503- 532, Springer, 2014.
  • Tamaz Tadumadze, Variation formulas of solution for controlled delay functional-differential equation taking into account delays perturbations and the mixed initial condition, Mem. Diff. Eq. Math. Phys. 58, 139-146, Tbilisi University Press, 2013.
  • Tamaz Tadumadze, On the existence of an optimal element in two-stage optimal problems with delays, Georgian Math. J., v. 20 , no. 3, 601-623, De Gruyter, 2013.
  • Tamaz Tadumadze, Optimization of initial data for linear neutral functional-differential equations with the discontinuous initial condition, Azerbaijan Journal of Mathematics, v. 2, No. 2 ,84-93., Institute of Mathematics and Mechanics NAS of Azerbaijan, 2012.
  • Tamaz Tadumadze, On a connection between controllability of the initial and perturbed two-stage systems, Semin. I. Vekua Instit. of Appl. Math., Rep., 38, 52-61, Tbilisi University Press, 2012.
  • Tamaz Tadumadze, On the optimality of initial element for delay functional differential equations with the mixed initial condition, Proc. I. Vekua Inst. of Appl. Math. 61-62 , 65- 71, Tbilisi University Press, 2012.
  • Tamaz Tadumadze, Variation formulas of solution for nonlinear delay differential equations with taking into account delay perturbation and discontinuous initial condition, Georgian International Journal of Sciences and Technology, v. 3, no. 1, 1-19, Nova Science Publishers, Inc., 2011.
  • Tamaz Tadumadze, Variation formulas of solution for a delay differential equation with taking into account delay perturbation and the continuous initial condition, Georgian Math. J. v.18, No. 2, 348-364, De Gruyter, 2011.
  • Tamaz Tadumadze, Abdeljalili Nachaoui, Variation formulas of solution for a controlled delay functional- differential equation considering delay perturbation, TWMS J. App. Eng. Math. V.1, N.1, 34- 44, Isic University, 2011.
  • Tamaz Tadumadze, Existence of optimal initial data and well-posedness with respect to functional for a neutral optimal problem, Sem. I. Vekua Inst. Appl. Math., Rep., v. 36-37, 38-41, Tbilisi University Press, 2011.
  • Tamaz Tadumadze, Nika Gorgodze, On effects of constant delay perturbation and the discontinuous initial condition in variation formulas of solution of delay controlled functional-differential equation, Sem. I. Vekua Inst. Appl. Math., Rep. , v. 36-37 , 81-97, Tbilisi University Press, 2011.
  • Tamaz Tadumadze, Akaki Arsenashvili, Optimal control of variable structure systems with delays and mixed intermediate condition, Functional Differential Equations. V. 17, No 3-4, 295-317, Ariel University Center of Samaria, 2010.
  • Tamaz Tadumadze, On the existence of an optimal element for a delay control problem, Nonlinear Analysis 73 , 211-220., Elsevier, 2010.
  • Tamaz Tadumadze, Formulas of variation for solutions of some classes of functional differential equations and their applications, Formulas of variation for solutions of some classes of functional differential equations and their applications, Elsevier, 2009.
  • Tamaz Tadumadze, An inverse problem for some classes of linear functional differential equations, J. App. and Comput. Math. V. 8, # 2, 239-250, Institute of Applied Mathematics of Baku State University, 2009.
  • Guram Kharatishvili, Tamaz Tadumadze, Optimal control problems with delays and mixed initial condition, J. Math. Sci. (N.Y), vol. 160, No. 2, 221- 245, Springer, 2009.
  • Tamaz Tadumadze, Akaki Arsenashvili, Existence of optimal initial data and well-posedness with respect to functional for a class of delay optimal problem, Sem. I. Vekua Inst. Appl. Math., Rep., 35, 71-73, Tbilisi University Press, 2009.
  • Akaki Arsenashvili, Tamaz Tadumadze, Abdeljalili Nachaoui, On approximate solving of a class of an inverse problem for the linear delay differential equations, Bull. Georg. Nati. Acad. Sci.,v.2, no. 2 ,24-28, Georgian Academy Press, 2008.
  • Tamaz Tadumadze, Akaki Arsenashvili, Optimization of a delay variable structure control system with mixed intermediate condition, Bull. Georg. Nati. Acad. Sci. v.2 , no. 3 , 22-26, Georgian Academy Press, 2008.
  • Tamaz Tadumadze, Optimization of delay controlled systems with non-fixed initial moment and mixed initial condition, Proc. I. Vekua Institute of Applied Mathematics, v. 58, 92-96, TSU, 2008.
  • Guram Kharatishvili, Tamaz Tadumadze, Variation formulas for solution of a nonlinear differential equation with time delay and mixed initial condition, J. Math. Sci. (N.Y.), v. 148, no. 3, 302- 330, Springer, 2008.
  • Tamaz Tadumadze, Akaki Arsenashvili, Ia Ramishvili, Linearized maximum principle for neutral-type, variable-structure optimal problems with delays in controls, J. Math. Sci. (N.Y), v.148, no. 3, 382- 398, Springer, 2008.
  • Guram Kharatishvili, Tamaz Tadumadze, Variation formulas of solutions and optimal control problems for differential equations with retarded argument, J. Math. Sci. ( N.Y.) , v.104, No. 1, 1- 175, Springer, 2007.
  • Guram Kharatishvili, Tamaz Tadumadze, Optimization of delay dynamical systems with mixed initial condition, Bull. Georg. Nati. Acad. Sci., v.1, no. 4 , 20-26, Georgian Academy Press, 2007.
  • Guram Kharatishvili, Tamaz Tadumadze, Formulas of variation for solving differential equations with delayed arguments and mixed initial conditions, Doklady Mathematics, v. 73, №3, 360- 362 (translation from Doklady Akademii Nauk, 2006, v. 408, №2, 171-173), Russian Academy of Sciences, 2006.
  • Guram Kharatishvili, Tamaz Tadumadze, Necessary optimality conditions for optimal control problems with delays and mixed initial conditions, Doklady Mathematics, v. 73, №3, 380- 383 (translation from Doklady Akademii Nauk, 2006, v. 408, №3, 313-316), Russian Academy of Sciences, 2006.
  • Tamaz Tadumadze, Akaki Arsenashvili, Ia Ramishvili, Necessary conditions of optimality for neutral variable structure optimal problems with discontinuous initial condition, Mem. Diff. Eq. Math. Phys. v. 39( 2006 ), 1-34, Publishing House GCI, 2006.
  • Tamaz Tadumadze, Akaki Arsenashvili, Ia Ramishvili, Necessary conditions of optimality for neutral variable structure optimal problems with discontinuous initial condition, Mem. Diff. Eq. Math. Phys. v. 39( 2006 ), 1-34, Publishing House GCI, 2006.
  • Tamaz Tadumadze, Optimal control of delayed variable structure systems with discontinuous initial condition, J. App. and Comput. Math. 4 , No.1, 48-53, Institute of Applied Mathematics of Baku State University, 2005.
  • Tamaz Tadumadze, Akaki Arsenashvili, Optimal control of delayed variable structure systems with discontinuous initial condition, J. App. and Comput. Math. 4 , No.1, 48-53, Institute of Applied Mathematics of Baku State University, 2005.
  • Guram Kharatishvili, Tamaz Tadumadze, Variation formulas for the solutions of delay differential equations with discontinuous initial conditions, Sb. Math. 196, No.8, 1137-1163 (translation from Mat. Sb. 196, No. 8, 49-74 , 2005, V. A. Steklov Institute of Mathematics of Russian Academy of Sciences, 2005.
  • Tamaz Tadumadze, Lela Alkhazishvili, Formulas of variation of solution for non-linear controlled delay differential equation with continuous initial condition, Mem. Diff. Eq. Math. Phys. 31, 83-97, Publishing House GCI, 2004.
  • Tamaz Tadumadze, Ia Ramishvili, Formulas of variation for a solution of neutral differential equations with continuous initial condition, Georgian Math. J. v. 11 , No.1, 155-175, De Gruyter, 2004.
  • Tamaz Tadumadze, Guram Kharatishvili, Well-posedness of the Cauchy problem for nonlinear differential equations with variable delays, Differ. Equ. 40, No.3, 360-369 (translation from Differ. Uravn. 40, No. 3, 338-345, 2004 ), Russian Academy of Sciences, 2004.
  • Tamaz Tadumadze, Guram Kharatishvili, Formulas for the variation of the solution of a differential equation with retarded arguments and with a continuous initial condition, Differ. Equ. 40, No.4, 542-551( translation from Differ. Uravn. 40, No.4, 500-508, 2004 ), Russian Academy of Sciences, 2004.
  • Tamaz Tadumadze, Lela Alkhazishvili, Formulas of variation of solution for nonlinear controlled delay differential equation with discontinuous initial condition, Mem. Diff. Eq. Math. Phys. 29 , 125-150, Publishing House GCI, 2003.
  • Tamaz Tadumadze, Nika Gorgodze, Guram Kharatishvili, Dynamic mathematical model of output of the production and neutral optimal control problem, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, 17(2), 36-38, TSU, 2002.