Algebraic approach to duality in optimization and applications
This work makes considerations of duality of optimization problems in a vector space without a topological structure. A strong duality relation is established by means of algebraic subdifferentials and algebraic conjugate functions. Without the lower semicontinuity or quasicontinuity hypothesis on perturbation functions, and by a purely algebraic approach, certain topological duality relations are obtained. Applications of the obtained results are given for the sum of two convex functions, monotropic problems and infinite convex or linear problems. Finally, algebraic constraint qualification for problems with countably infinitely many inequality constraints, are also obtained.
scientific article; zbMATH DE number 7383625
scientific article