Abstract:

In recent work, Anitescu has proposed constraint relaxation to deal with the problem of unbounded multipliers when trying to solve nonlinear complementarity problems as nonlinear programming problems. Recent work has shown this is a very efficient technique to solve both pure complementarity problems and mathematical programs with equilibrium constraints (MPEC�s) with interior-point codes for nonconvex nonlinear programming. The work has been extended to algorithms for warmstarting interior-point codes for both linear and nonlinear programming. Another advantage of constraint relaxation is that it provides a means to determine when a nonlinear programming problem is infeasible. It also can provide better approximation of strict minima that are not KKT points. The talk discusses all of these advances, and provides results from substantial numerical testing demonstrating the effectiveness of the methods.