Algebraic Approach to Duality in Optimization and Applications

This paper studies duality of optimization problems in a vector space without topological structure. A strong duality relation is established by means of algebraic subdifferential and algebraic conjugate functions. Topological duality relations are obtained by the algebraic approach without lower semicontinuity or quasicontinuity hypothesis on perturbation functions. Applications are given for the sum of two convex functions, monotropic problems, infinite convex or linear problems. Attention is also made on the algebraic constraint qualification for problems with countably infinitely many inequality constraints.