Optimality conditions for nonconvex semidefinite programming
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.