A class of nonconvex semidefinite programming in which every KKT point is globally optimal

We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush–Kuhn–Tucker (KKT) conditions is globally optimal despite nonconvexity. This property is related to pseudoconvex optimization. This class of problems is motivated by an eigenfrequency topology optimization problem in structural engineering, but is presented in a more general form.