Optimality conditions for nonconvex semidefinite programming

Anders Forsgren

This paper concerns nonlinear semidefinite programming problems for which no convexity assumptions can be made. We derive first- and second-order optimality 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.

To appear in Mathematical Programming, 2000.

Contact: andersf@math.kth.se