Abstract
A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its -approximate solutions, and then we prove -weak duality theorem and -strong duality theorem which hold between the problem and its Wolfe type dual problem. Moreover, we give an example illustrating the duality theorems.
Highlights
Convex semidefinite optimization problem is to optimize an objective convex function over a linear matrix inequality
Jeyakumar and Glover 11 gave -optimality conditions for convex optimization problems, which hold without any constraint qualification
Kim and Lee 12 proved sequential -saddle point theorems and -duality theorems for convex semidefinite optimization problems which have not conic constraints
Summary
A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its -approximate solutions, and we prove -weak duality theorem and -strong duality theorem which hold between the problem and its Wolfe type dual problem. We give an example illustrating the duality theorems
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