Characterizations of optimality without constraint qualification for the abstract convex program
We consider the general abstract convex program (P) minimize f(x), subject to g(x)∈−S, where f is an extended convex functional on X, g: X→Y is S-convex, S is a closed convex cone and X and Y are topological linear spaces. We present primal and dual characterizations for (P). These characterizations are derived by reducing the problem to a standard Lagrange multiplier problem. Examples given include operator constrained problems as well as semi-infinite programming problems.
Key wordsCone-convex Locally Convex Topological Vector Space Optimality Conditions Subdifferential Directional Derivative Faithfully Convex Lagrange Multipliers Slater’s Condition Semi-infinite Programs
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