The penalty interior-point method fails to converge
- 1 August 2005
- journal article
- research article
- Published by Taylor & Francis in Optimization Methods and Software
- Vol. 20 (4-5) , 559-568
- https://doi.org/10.1080/10556780500140078
Abstract
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A popular method for solving MPCCs is the penalty interior-point algorithm (PIPA). This paper presents an example for which PIPA converges to a nonstationary point, providing a counterexample to the established theory. The reasons for this adverse behavior are discussed.Keywords
All Related Versions
This publication has 12 references indexed in Scilit:
- Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraintsMathematical Programming, 2004
- Solving mathematical programs with complementarity constraints as nonlinear programsOptimization Methods and Software, 2004
- A likelihood-MPEC approach to target classificationMathematical Programming, 2003
- Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity ConstraintsSIAM Journal on Optimization, 2001
- Strategic gaming analysis for electric power systems: an MPEC approachIEEE Transactions on Power Systems, 2000
- Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and SensitivityMathematics of Operations Research, 2000
- Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming ProblemsSIAM Journal on Control and Optimization, 1998
- Some Feasibility Issues in Mathematical Programs with Equilibrium ConstraintsSIAM Journal on Optimization, 1998
- Engineering and Economic Applications of Complementarity ProblemsSIAM Review, 1997
- Convex two-level optimizationMathematical Programming, 1988