Total Lagrange duality for DC infinite optimization problems

Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces

We consider the DC (difference of two convex functions) optimization problem ðPÞ inf x∈Xfðf 1ðxÞ− f 2ðxÞÞ þ ðg1ðAxÞ− g2ðAxÞÞg, where f 1, f 2, g1, and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y , and A is a linear continuous operator from X to Y . Adopting different tactics, two types of the Fenchel dual problems of ðPÞ are given. By usi...

Duality and Optimality Conditions for Infinite Dimensional Optimization Problems

Using a nonsymmetric duality for abstract continuous convex control problems opti-mality conditions are derived for calculating the primal and dual solutions in the case of linear on state depending dual operators. Functional and pointwise conditions are considered. Subject: 49K22, 49K27, 49N15, 90C42. Keywords: abstract optimal control , nonsymmetric duality, suucient conditions of optimality,...

WEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces

We give new regularity conditions for convex optimization problems in separated locally convex spaces. We completely characterize the stable strong and strong Fenchel-Lagrange duality. Then we give similar statements for the case when a solution of the primal problem is assumed as known, obtaining complete characterizations for the so-called total and, respectively, stable total Fenchel-Lagrang...

Stable Zero Lagrange Duality for DC Conic Programming