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Semidefinite concave programming. (English) Zbl 1296.90086

Summary: We introduce so-called semidefinite concave programming or equivalently semidefinite convex maximization problem. We derive new global optimality conditions by generalizing A. S. Strekalovsky’s theorem [J. Glob. Optim. 12, No. 4, 415–434 (1998; Zbl 0908.90243)]. Based on the global optimality conditions, we construct an algorithm which generates a sequence of local maximizers converging to the global solution. Subproblems of the proposed algorithm are semidefinite linear programming.

MSC:

90C22 Semidefinite programming
90C26 Nonconvex programming, global optimization

Citations:

Zbl 0908.90243
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