Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints

Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived...

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Main Authors: Liu, X., Sun, Jie
Format: Journal Article
Language:English
Published: Springer 2004
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/91445
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author Liu, X.
Sun, Jie
author_facet Liu, X.
Sun, Jie
author_sort Liu, X.
building Curtin Institutional Repository
collection Online Access
description Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. © Springer-Verlag 2004.
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spelling curtin-20.500.11937-914452023-04-20T04:34:24Z Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints Liu, X. Sun, Jie Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics global convergence interior-point methods mathematical programming with equilibrium constraints stationary point VARIATIONAL INEQUALITY CONSTRAINTS LINEAR COMPLEMENTARITY CONSTRAINTS OPTIMIZATION PROBLEMS BILEVEL ALGORITHM CONVERGENCE OPTIMALITY Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. © Springer-Verlag 2004. 2004 Journal Article http://hdl.handle.net/20.500.11937/91445 10.1007/s10107-004-0543-6 English Springer fulltext
spellingShingle Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
global convergence
interior-point methods
mathematical programming with equilibrium constraints
stationary point
VARIATIONAL INEQUALITY CONSTRAINTS
LINEAR COMPLEMENTARITY CONSTRAINTS
OPTIMIZATION PROBLEMS
BILEVEL
ALGORITHM
CONVERGENCE
OPTIMALITY
Liu, X.
Sun, Jie
Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title_full Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title_fullStr Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title_full_unstemmed Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title_short Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
title_sort generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
topic Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
global convergence
interior-point methods
mathematical programming with equilibrium constraints
stationary point
VARIATIONAL INEQUALITY CONSTRAINTS
LINEAR COMPLEMENTARITY CONSTRAINTS
OPTIMIZATION PROBLEMS
BILEVEL
ALGORITHM
CONVERGENCE
OPTIMALITY
url http://hdl.handle.net/20.500.11937/91445