OPTIMALITY CONDITIONS FOR NONCONVEXSEMIDEFINITE PROGRAMMINGAnders

This paper concerns nonlinear semideenite programming problems for which no convexity assumptions can be made. We derive rst-and second-order op-timality conditions analogous to those for nonlinear programming. Using techniques analogous to those used in nonlinear programming, we extend existing theory to cover situations where strict complementarity does not hold and the constraint matrix is structurally sparse. The regularity conditions used are consistent with those of nonlinear programming in the sense that the conventional optimality conditions for nonlinear programming are obtained when the constraint matrix is diagonal.