A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints

In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer–Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation....

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 172; no. 1; pp. 222 - 244
Main Authors: Zhu, Z.B., Zhang, K.C.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 2006
Elsevier
Subjects:
Applied sciences
Calculus of variations and optimal control
Exact sciences and technology
Global convergence
Mathematical analysis
Mathematical programming
Mathematical programs with equilibrium constraints
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
SQP algorithm
Successive approximation
Superlinear convergence rate
System of linear equations
System of linear equations
Successive approximation
Global convergence
Superlinear convergence rate
Mathematical programs with equilibrium constraints
SQP algorithm
Convergence acceleration
Numerical linear algebra
Optimization method
Complementarity problem
Linear complementarity problem
Algorithm
Constrained optimization
Equation system
Equilibrium constraint
Direct method
Linear system
Matrix inversion
Applied mathematics
Convergence rate
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Description
Summary:In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer–Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation. The smooth optimization is solved by SQP algorithm for standard constrained optimization. Global convergence and superlinear convergence rate are established under some suitable assumptions. Moreover, we conclude that the current iterate point is an exact stationary point of the MPEC problem when the proposed algorithm stops in finite iteration.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.01.141