Application of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative relaxation for mixed binary nonconvex quadratic optimization problems

Mirai Tanaka, Kazuhide Nakata, Hayato Waki

Research output: Contribution to journalArticle

Abstract

In this paper, we propose an effective approach to solve doubly nonnegative relaxation (DNR) problems for mixed binary nonconvex quadratic optimization problems. In our approach, we convert a given DNR problem into another one that is smaller than the original one by exploiting degeneracy. We can expect numerical stability of primal-dual interior-point methods for the DNR problem to be improved because this conversion can be regarded as a partial application of a facial reduction algorithm. Moreover, we propose an inexact primal-dual path-following method for the resulting DNR problems. In our algorithm, to compute search directions, we solve large linear systems via the preconditioned symmetric quasi-minimal residual (PSQMR) method. To accelerate the convergence of the PSQMR method, we propose three preconditioners. Numerical results presented in this paper show that we can solve some instances of DNR problems quickly and accurately.

Original languageEnglish
Pages (from-to)699-724
Number of pages26
JournalPacific Journal of Optimization
Volume8
Issue number4
Publication statusPublished - Oct 2012

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Path-following Methods
Primal-dual Method
Quadratic Optimization
Nonconvex Optimization
Non-negative
Binary
Optimization Problem
Convergence of numerical methods
Minimal Residual Method
Linear systems
Primal-dual Interior Point Method
Numerical Stability
Degeneracy
Preconditioner
Accelerate
Convert
Linear Systems
Partial
Numerical Results

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization

Cite this

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