Title: An Active Set Method for Large-Scale Constrained Optimization

Speaker: Prof. Richard H. Byrd, University of Colorado
                              
Date/Time: Thursday, February 3, 2005, 10:00-11:00 a.m. (PT)

Location: Building 980, Room 95 (Sandia NM), Building 921, Room 137 (Sandia CA)

Brief Abstract: The two dominant approaches for solving nonlinear inequality constrained optimization problems are currently interior point methods and active set methods. However, the principle active set approach, successive quadratic programming, is limited in the number of free variables it can handle. Interior point methods can currently handle much larger problems, but have certain weaknesses, especially when warm starts are available.
                                                                                       
This issue has motivated us to develop SLIQUE, an active set algorithm that uses a linear programming model rather than quadratic programming to deal with inequalities. After solution of a linear programming subproblem has selected a working set, SLIQUE minimizes a quadratic approximation of the Lagrangian subject to the selected equality constraints.
                                                                                      
To force convergence from infeasible starting points SLIQUE uses an exact nondifferentiable penalty function. To determine the penalty parameter, we use an LP subproblem. We have developed a more powerful global convergence theory for exact penalty methods based on this procedure.