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Full-Text Articles in Physical Sciences and Mathematics
Optimization Of Delay-Differential Inclusions Of Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang
Optimization Of Delay-Differential Inclusions Of Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang
Mathematics Research Reports
No abstract provided.
Optimal Control Of Delay-Differential Inclusions With Multivalued Initial Conditions In Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang
Optimal Control Of Delay-Differential Inclusions With Multivalued Initial Conditions In Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang
Mathematics Research Reports
This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the …
Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich
Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational …
Variational Analysis Of Evolution Inclusions, Boris S. Mordukhovich
Variational Analysis Of Evolution Inclusions, Boris S. Mordukhovich
Mathematics Research Reports
The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such roblems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of Asplund (and hence any reflexive Banach) spaces. In this way we establish extended results on stability of discrete approximations (with the strong W^1,2-convergence of optimal solutions under consistent perturbations of …