Some properties of regularization and penalization schemes for MPECs
- 1 October 2004
- journal article
- other
- Published by Taylor & Francis in Optimization Methods and Software
- Vol. 19 (5), 527-556
- https://doi.org/10.1080/10556780410001709439
Abstract
Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In the penalized formulation, the complementarity constraint appears as a penalty term in the objective. The existence and uniqueness of solutions for these formulations are investigated, and estimates are obtained for the distance of these solutions to the MPEC solution under various assumptions.Keywords
This publication has 17 references indexed in Scilit:
- An Implementable Active-Set Algorithm for Computing a B-Stationary Point of a Mathematical Program with Linear Complementarity ConstraintsSIAM Journal on Optimization, 2002
- Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity ConstraintsSIAM Journal on Optimization, 2001
- Exact Penalization of Mathematical Programs with Equilibrium ConstraintsSIAM Journal on Control and Optimization, 1999
- A smoothing method for mathematical programs with equilibrium constraintsMathematical Programming, 1999
- Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming ProblemsSIAM Journal on Optimization, 1997
- The nonlinear bilevel programming problem:formulations,regularity and optimality conditionsOptimization, 1995
- Generalized equations and their solutions, part II: Applications to nonlinear programmingPublished by Springer Nature ,1982
- First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problemsMathematical Programming, 1979
- A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programmingMathematical Programming, 1977
- Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear SystemsSIAM Journal on Numerical Analysis, 1976