We introduce so-called semidefinite quasiconvex maximization problem. We derive new global optimality conditions by generalizing [9]. Using these conditions, we construct an algorithm which generates a sequence of local maximizers that converges to a global solution. Also, new applications of semidefinite quasiconvex maximization are given. Subproblems of the proposed algorithm are semidefinite linear programming.

MSC

90C26, 93C05

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