Approximation and Optimization of Polyhedral Discrete and Differential Inclusions
In the first part of the paperoptimization of polyhedral discrete and differential inclusions is considered, the problem is reduced to convex minimization problem and the necessary and sufficient condition for optimality is derived. The optimality conditions for polyhedral differential inclusions based on discrete-approximation problem according to continuous problems are formulated. In particular, boundedness of the set of adjoint discrete solutions and upper semicontinuity of the locally adjoint mapping are proved. In the second part of paper an optimization problem described by convex inequality constraint is studied. By using the equivalence theorem concerning the subdifferential calculus and approximating method necessary and sufficient condition for discrete-approximation problem with inequality constraint is established.
KeywordsSet-valued polyhedral inequality constraint dual cone subdifferential discrete-approximation uniformly bounded upper semicontinuous
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- 2.Mahmudov, E.N., Pshenichnyi, B.N.: Necessary condition of extremum and evasion problem, pp. 3–22. Preprint, Institute Cybernetcis of Ukraine SSR, Kiev (1978)Google Scholar
- 8.Makarov, V.L., Rubinov, A.M.: The Mathematical Theory of Economic Dynamics and Equilibrium, Nauka, Moscow (1977); English transl., Springer, Berlin (1973)Google Scholar
- 9.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory; II: Applications, Grundlehren Series. Fundamental Principles of Mathematical Sciences, vol. 330, 331. Springer (2006)Google Scholar
- 10.Pshenichnyi, B.N.: Convex analysis and extremal problems, Nauka, Moscow (1980)Google Scholar