Optimality conditions for rank-constrained matrix optimization. (English) Zbl 1438.90272

Summary: In this paper, we comprehensively study optimality conditions for rank-constrained matrix optimization (RCMO). By calculating the Clarke tangent and normal cones to a rank-constrained set, along with the given Fréchet, Mordukhovich normal cones, we investigate four kinds of stationary points of the RCMO and analyze the relations between each stationary point and local/global minimizer of the RCMO. Furthermore, the second-order optimality condition of the RCMO is achieved with the help of the Clarke tangent cone.


90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming


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