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A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming

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  • Aiqun Huang
  • Chengxian Xu

Abstract

When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.

Suggested Citation

  • Aiqun Huang & Chengxian Xu, 2012. "A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-13, August.
    • Handle: RePEc:hin:jnlmpe:819607
    DOI: 10.1155/2012/819607
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