Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Authors:
Hande Y. Benson;Arun Sen;David F. Shanno;Robert J. Vanderbei
Affiliations:
Decision Sciences Department, LeBow College of Business, Drexel University, Philadelphia 19104;Department of Operations Research and Financial Engineering, Princeton University, Princeton 08544;RUTCOR - Rutgers Center of Operations Research, Rutgers University, New Brunswick 08903;Department of Operations Research and Financial Engineering, Princeton University, Princeton 08544
Venue:
Computational Optimization and Applications
Year:
2006

Citing 10
Cited 8

Engineering and Economic Applications of Complementarity Problems

SIAM Review
An Interior-Point Algorithm for Nonconvex Nonlinear Programming

Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity

Mathematics of Operations Research
Test Examples for Nonlinear Programming Codes

Test Examples for Nonlinear Programming Codes
On the Global Convergence of a Filter--SQP Algorithm

SIAM Journal on Optimization
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

SIAM Journal on Optimization
Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity Constraints

SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming

SIAM Journal on Optimization
An Infeasible-Interior-Point Method for Linear Complementarity Problems

SIAM Journal on Optimization
Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions

Computational Optimization and Applications

An exact primal---dual penalty method approach to warmstarting interior-point methods for linear programming

Computational Optimization and Applications
Interior-point methods for nonconvex nonlinear programming: regularization and warmstarts

Computational Optimization and Applications
Optimization and dynamical systems algorithms for finding equilibria of stochastic games

Optimization Methods & Software
A Complementarity Constraint Formulation of Convex Multiobjective Optimization Problems

INFORMS Journal on Computing
Multi-vehicle path coordination in support of communication

ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Primal-dual interior-point method for thermodynamic gas-particle partitioning

Computational Optimization and Applications
The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints

Mathematics of Operations Research
An $\ell_1$ Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the question of solving equilibrium problems--formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPECs)--as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties and provide substantial numerical results. We go on to show that penalty methods can resolve some problems that interior-point algorithms encounter in general.