Optimization with Semidefinite, Quadratic and Linear Constraints

Farid Alizadeh and Stefan Schmieta

We consider optimization problems where variables have either linear, or convex quadratic or semidefinite constraints. First, we define 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.

RUTCOR, RRR Report 23-97, November 1997, 640 Bartholomew Rd, Piscataway NJ 08854.

Contact: alizadeh@rutcor.rutgers.edu