Article ID: | iaor20011535 |
Country: | United States |
Volume: | 37 |
Issue: | 2 |
Start Page Number: | 617 |
End Page Number: | 652 |
Publication Date: | Feb 1999 |
Journal: | SIAM Journal on Control and Optimization |
Authors: | Stoer Mechthild, Scholtes S. |
Keywords: | penalty functions |
We study theoretical and computational aspects of an exact penalization approach to mathematical programs with equilibrium constraints (MPECs). In the first part, we prove that a Mangasarian–Fromovitz-type condition ensures the existence of a stable local error bound at the root of a real-valued nonnegative piecewise smooth function. A specification to nonsmooth formulations of equilibrium constraints, e.g., complementarity conditions or normal equations, provides conditions which guarantee the existence of a nonsmooth exact penalty function for MPECs. In the second part, we study a trust region minimization method for a class of composite nonsmooth functions which comprises exact penalty functions arising from MPECs. We prove a global convergence result for the general method and incorporate a penalty update rule. A further specification results in an SQP trust region method for MPECs based on an L