DC semidefinite programming and cone constrained DC optimization II: local search methods

In this paper, we study possible extensions of the main ideas and methods constrained DC optimization to case nonlinear semidefinite programming problems more general nonsmooth cone problems. first part analyse two different approaches definition matrix-valued functions (namely, order-theoretic componentwise), some properties convex mappings demonstrate how compute decompositions constraints appearing in applications. We also a decomposition maximal eigenvalue function. This can be used reformulate as inequality constrains. Finally, local optimality conditions for The second paper is devoted detailed convergence analysis well-known DCA method solving (Difference Convex functions) global present comprehensive version utilizing exact penalty functions. particular, exactness property penalized subproblems provide types sufficient feasible critical point problem from an infeasible starting point. numerical section work, applied computing compressed modes variational sphere packing on Grassmannian.