Optimization with Semidefinite, Quadratic and Linear Constraints

We consider optimization problems where variables have either linear, or convex quadratic or semideenite constraints. First, we deene and characterize primal and dual nondegeneracy and strict complementarity conditions. Next, we develop primal-dual interior point methods for such problems and show that in the absence of degeneracy these algorithms are numerically stable. Finally we describe an implementation of our method and present numerical experiments with both degenerate and nondegenerate problems.