Vladimir S. Variational problems and generalized optimization of linear systems

New results about genericity of solvability nonconvex extremal problems which depend on parameters are obtained. The new variant of Deville-Godefroy-Zizler principle for vector optimization problems in metric spaces is proved. New solvability theorems for convex functionals maximization on convex bounded subsets of Banach spaces are obtained. A theory of generalized solvability for convex minimization problems is developed. Numerical algorithms of solving of nonconvex linear distributed systems generalized optimization problems are offered and investigated. A theory for numerical and analytical analysis of vector optimization problems of linear distributed systems is developed. Generalized solutions existence and controllability properties of the parabolic, pseudoparabolic and parabolic-hyperbolic models with the interface conditions are investigated. Generalization of Vishik-Lax-Milgram theorem is obtained. An approach for generalized solvability of operator equations in uniform spaces is offered.