Approximate Optimality Conditions for Composite Convex Optimization Problems
Tóm tắt
The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces, where all functions involved are not necessarily lower semi-continuous. By using the properties of the epigraph of conjugate functions, we introduce a new regularity condition and give its equivalent characterizations. Under this new regularity condition, we derive necessary and sufficient optimality conditions of
$$\varepsilon $$
-optimal solutions for the composite convex optimization problem. As applications of our results, we derive approximate optimality conditions to cone-convex optimization problems. Our results extend or cover many known results in the literature.
Từ khóa
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