Accès libre

Control and optimization of abstract continuous time evolution inclusions

À propos de cet article

Citez

Ahmed, N.U. and Teo, K.L. (1981) Optimal Control of Distributed Parameter Systems. North Holland. Search in Google Scholar

Amir, A. and Mokhtar-Kharroubi, H. (2010) Normality and Quasiconvex Integrands. J. Convex Analysis. 17, 1, 59-68. Search in Google Scholar

Andrews, K., Kuttler, K., Li, J. and Shillor, M. (2019) Measurable solution for elliptic inclusion and quasistatic problems. Comput. Math. Appl. 77, 2869-2882. Search in Google Scholar

Andrews, K., Kuttler, K. and Li, J. (2020) Measurable solutions to General Evolution Inclusion. Evolution Equations and Control Theory. 9, 4, 935-960. Search in Google Scholar

Aubin, J. P. (1972) Théorèmes de minimax pour une classe de fonctions. C.R. Acad. Sci. Paris Sér. A, 274, 455-458. Search in Google Scholar

Aubin, J. P. and Cellina, A. (1984) Differential Inclusions. Springer-Verlag. Search in Google Scholar

Aubin, J. P. and Clarke, F.H. (1979) Shadow prices and duality for a class of optimal control problems. SIAM J. Cont. and Optim. 17, 5. 567-586. Search in Google Scholar

Aubin, J. P. and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley. Search in Google Scholar

Barbu, V. (1976) Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordho, Leyden. Search in Google Scholar

Barbu, V. (1994) Mathematical Methods of Differential Systems. Kluwer Academic Publishers. Search in Google Scholar

Barbu, V. and Precupanu, Th. (1978) Convexity and Optimization. Sijtho -Noordho. Search in Google Scholar

Benharath, M. and Mokhtar-Kharroubi, H. (2010) Exterior Penalty in Optimal Control Problems with State-Control Constraints. Rendiconti del Circolo Mathematico di Palermo. 59, 3, 389-403. Search in Google Scholar

Bian, W. and Weeb, J.R.L. (1999) Solutions of nonlinear evolution inclusions. Nonlinear Analysis 37, 915-932. Search in Google Scholar

Bot, R.I. and Csetnek, E. R. (2012) Regularity conditions via generalized interiority notions in convex optimization: new achievements and their relation to some classical statements. Optimization 61 (1), 35-65. Search in Google Scholar

Bressan, A. and Zhang, D. (2012) Control Problems for a class of Set valued Evolutions. Set Valued Var. Anal. 20: 581-601. Search in Google Scholar

Castaing, C. and Valadier, M. (1977) Convex Analysis and Measurable Multifunctions. Lecture Notes 580. Springer Verlag. Search in Google Scholar

Denkowski, Z., Migorski, S. and Papageorgiou, N.S. (2003) On convergence of solutions of multivalued parabolic equations and applications. Nonlinear Anal. 54, 667-682. Search in Google Scholar

Fiacca, A., Papageorgiou, N.S. and Papalini, F. (1998) On the existence of optimal control for nonlinear infinite dimensional systems. Czech. Math. J. 49, 2, 291-312. Search in Google Scholar

Han, W. and Sofonea, M. (2003) Quasistatic contact problems in viscoelasticity and viscoplasticity. In: AMS/IP Studies in Advanced Math. 30. Amer. Math Soc. Providence RI; International Press, Somerville, MA. Search in Google Scholar

Kuttler, K. L. (2000) Nondegenerate implicit evolution inclusion. Electron. J. Differential Equations. 2000, 1-20. Search in Google Scholar

Kuttler, K. L. (2019) Measurable solutions for Elliptic and Evolution inclusions. EECT. doi;10.3934/cect.2020041 Search in Google Scholar

Kuttler, K. L. and Li, J. (2015) Measurable solution for stochastic evolution equations without uniqueness. Appl. Anal., 94, 2456-2477. Search in Google Scholar

Kuttler, K. L., Li, J. and Shillor, M. (2016) A general product measurability theorem with applications to variational inequalities. Elect. J. Di . Equa., 2016, 90, 1–12. Search in Google Scholar

Kuttler, K. L. and Shillor, M. (1999) Set-valued pseudomonotone maps and degenerate evolution inclusions. Commun. Contemp. Math. 1, 87-123. Search in Google Scholar

Mahmudov, E. N. (2011) Approximation and Optimization of Discrete and Differential Inclusions, Elsevier, Boston, USA. Search in Google Scholar

Migorski S., Ochal, A. and Sofonea, M. (2013) Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems. Advances in Mechanics and Mathematics, 26, Springer, New York. Search in Google Scholar

Mokhtar-Kharroubi, H. (1987) Sur quelques fonctions marginales et leurs applications. Thèse Doctorat Es-Sciences. Lille I. Search in Google Scholar

Mokhtar-Kharroubi, H. (2017) Convex and convex-like optimization over a range inclusion problem and first applications. Decisions in Economics and Finance 40, 1. Search in Google Scholar

Mokhtar-Kharroubi, H. (2022) Characterizations and classification of para-convex multimaps. Control & Cybernetics, 51, 3. Search in Google Scholar

Motreanu, D. and Radulescu, V. (2003) Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems. Kluwer Acad. Publ. Search in Google Scholar

Oppezzi, P. and Rossi, A. M. (1995) Existence results for unilateral problems with multivalued operators. J. Convex Anal 2, 1/2, 241-261. Search in Google Scholar

Papageorgiou, N. S. (1987) On the attainable set of Differential Inclusion and Control systems. J. Math. Anal. Appl. 125, 305-322. Search in Google Scholar

Papageorgiou, N. S. (1991) On the dependance of the solutions and optimal solutions of control problems on the control constraint set. J. Math. Anal. Appl. 158, 427-447. Search in Google Scholar

Peypouquet, J. and Sorin, S. (2009) Evolution equations for maximal operators. Asymptotic analysis in continuous and discrete-time. Math. OCJ. 08 May. Search in Google Scholar

Ravikumar, K., Mohan, M. T. and Anguraj, A. (2021) Apprioximate controllability of a non-Autonomous evolution equation in Banach Spaces. Numerical Algebra Control and Optimization. doi:10.3934/naco.2020038 Search in Google Scholar

Robinson, S. (1976) Regularity and stability for convex multivalued functions. Math. Oper. Res, 1, 2, 130-143. Search in Google Scholar

Ursescu, C. (1975) Multifunctions with convex closed graph. Czechoslovak Mathematical Journal, 3, 438-441. Search in Google Scholar

Vilches, E. and Nguiven, B.T. (2020) Evolution equation governed by time-dependant monotone operator with full domain. Set-Valued and Variational Analysis, 28, 569–581. Search in Google Scholar

Wagner, D. (1977) Survey on measurable selections theorems. SIAM. J. Cont. Optim. 15, 850-903. Search in Google Scholar

Zagurovsky, M. Z., Mel’nik, V. S. and Kasyanov, P. O. (2011) Evolution Equations and Variational Inequalities for Earth Data Processing II. Springer. Search in Google Scholar