Exact Penalization of Mathematical Programs with Equilibrium Constraints

Authors:
Stefan Scholtes;Michael Stöhr
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1999

Citing 0
Cited 14

Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints

Computational Optimization and Applications
A new branch and bound algorithm for solving quadratic programs with linear complementarity constraints

Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience

Computational Optimization and Applications
A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints

Computational Optimization and Applications
Newton-Type method for a class of mathematical programs with complementarity constraints

Computers & Mathematics with Applications
Classification model selection via bilevel programming

Optimization Methods & Software - Mathematical programming in data mining and machine learning
Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints

Computational Optimization and Applications
On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints

Journal of Global Optimization
Infeasibility Detection and SQP Methods for Nonlinear Optimization

SIAM Journal on Optimization
A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints

SIAM Journal on Optimization
Mathematical Programs with Equilibrium Constraints: Enhanced Fritz John-conditions, New Constraint Qualifications, and Improved Exact Penalty Results

SIAM Journal on Optimization
The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints

Mathematics of Operations Research
Optimality Conditions via Exact Penalty Functions

SIAM Journal on Optimization
A trust region algorithm for nonlinear bilevel programming

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 \(\ell_1\) penalty function.