A superlinear infeasible-interior-point algorithm for monotone complementarity problems

doi:https://doi.org/10.2172/406125

Title: A superlinear infeasible-interior-point algorithm for monotone complementarity problems

Full Record
Other Related Research

Abstract

We use the globally convergent framework proposed by Kojima, Noma, and Yoshise to construct an infeasible-interior-point algorithm for monotone nonlinear complementary problems. Superlinear convergence is attained when the solution is nondegenerate and also when the problem is linear. Numerical experiments confirm the efficacy of the proposed approach.

Authors:

Wright, S ^[1]; Ralph, D ^[2]

Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
Melbourne Univ., Parkville, VIC (Australia). Dept. of Mathematics

Publication Date:: 1996-11-01

Research Org.:: Argonne National Lab., IL (United States)

Sponsoring Org.:: USDOE Office of Energy Research, Washington, DC (United States)

OSTI Identifier:: 406125

Report Number(s):: MCS-P-344-1292
ON: DE97000553

DOE Contract Number:: W-31109-ENG-38

Resource Type:: Technical Report

Resource Relation:: Other Information: PBD: [1996]

Country of Publication:: United States

Language:: English

Subject:: 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; NONLINEAR PROBLEMS; ALGORITHMS; CONVERGENCE; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; ITERATIVE METHODS

Citation Formats


                    Wright, S, and Ralph, D. A superlinear infeasible-interior-point algorithm for monotone complementarity problems.  United States: N. p., 1996. 
        Web.  doi:10.2172/406125.

Copy to clipboard


                    Wright, S, & Ralph, D. A superlinear infeasible-interior-point algorithm for monotone complementarity problems.  United States.  https://doi.org/10.2172/406125

Copy to clipboard


                    Wright, S, and Ralph, D. Fri .  
        "A superlinear infeasible-interior-point algorithm for monotone complementarity problems".  United States.  https://doi.org/10.2172/406125.  https://www.osti.gov/servlets/purl/406125.

Copy to clipboard


                    
@article{osti_406125,

  title        = {A superlinear infeasible-interior-point algorithm for monotone complementarity problems},

  author       = {Wright, S and Ralph, D},

  abstractNote = {We use the globally convergent framework proposed by Kojima, Noma, and Yoshise to construct an infeasible-interior-point algorithm for monotone nonlinear complementary problems. Superlinear convergence is attained when the solution is nondegenerate and also when the problem is linear. Numerical experiments confirm the efficacy of the proposed approach.},

  doi          = {10.2172/406125},

  url          = {https://www.osti.gov/biblio/406125},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {1996},

  month        = {11}

}

Copy to clipboard

Technical Report:

View Technical Report (1.45 MB)

https://doi.org/10.2172/406125

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

A superlinearly convergent infeasible-interior-point algorithm for geometrical LCPs without a strictly complementary condition

Conference Mizuno, S

Some of interior-point algorithms have superlinear convergence. When solving a LCP (linear complementarity problem), superlinear convergence had been achieved under the assumption that a strictly complementary solution exists, whether starting from a feasible or an infeasible interior point. In this paper, we propose an algorithm for solving monotone geometrical LCPS, and we prove its superlinear convergence without the strictly complementary condition. The algorithm can start from an infeasible interior point and has globally linear convergence. When we use a big initial point or an almost feasible initial point, the algorithm has polynomial time convergence.
An O((k + 1){sup 2}nL) infeasible-interior-point

Conference Ji, Jun ; Potra, F ; Sheng, R

The P*-matrix linear complementarity problem requires the computation of a vector pair (x, s) {element_of} R{sup n{times}n} is a P*-matrix. The class of P*-matrices was introduced by Kojima, Megiddo, Noma and Yoshise and it contains many types of matrices (positive) semi-definite matrices and P-matrices, etc. Most interior-point methods for linear programming have been successfully extended to the monotone LCP, a special case of P*-matrix LCP. A potential reduction method for P{sub *}-matrix LCP was proposed by Kojima et al. Their method solves the LCP in at most O((1 + k) {radical}nL) iterations. However, no superliner convergence results have been provedmore »« less
Polynomial complexity and superlinear convergence of infeasible-interior-point algorithms

Conference Potra, F

Until very recently all theoretical results for interior-point-methods for linear programming have been proved under the assumption that a feasible interior point was given in advance. However, practical algorithms use starting points that lie in the interior of the region defined by the inequality constraints, but do not satisfy the equality constraints. The name infeasible-interior-point algorithm has been suggested to describe this type of method. The convergence of such algorithms was an open problem until recently, but a lot of new results have been obtained over the last couple of years. We will present a survey of the most significantmore »« less
Superlinear convergence of an interior-point method for monotone variational inequalities

Conference Ralph, D ; Wright, S

We describe an infeasible-interior-point algorithm for monotone variational inequality problems and prove that it converges globally and superlinearly under standard conditions plus a constant rank constraint qualification. The latter condition represents a generalization of the two types of assumptions made in existing superlinear analyses; namely, linearity of the constraints and linear independence of the active constraint gradients.
Full Text Available
Local convergence of interior-point algorithms for degenerate LCP

Conference Monteiro, R D.C. ; Wright, S

Most asymptotic convergence analysis of interior-point algorithms for monotone linear complementarily problems assumes that the problem is nondegenerate, that is, the solution set contains a strictly complementary solution. We investigate the behavior of these algorithms when this assumption is removed. We show that a large class of infeasible-interior point algorithms can not achieve superlinear convergence when the LCP is degenerate. We also give a feasible interior-point algorithm for degenerate monotone LCP with a reasonable linear rate, depending on the {open_quotes}size{close_quotes} of the degeneracy.

Similar Records