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An affine scaling method for optimization problems with polyhedral constraints

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  • William Hager
  • Hongchao Zhang

Abstract

Recently an affine scaling, interior point algorithm ASL was developed for box constrained optimization problems with a single linear constraint (Gonzalez-Lima et al., SIAM J. Optim. 21:361–390, 2011 ). This note extends the algorithm to handle more general polyhedral constraints. With a line search, the resulting algorithm ASP maintains the global and R-linear convergence properties of ASL. In addition, it is shown that the unit step version of the algorithm (without line search) is locally R-linearly convergent at a nondegenerate local minimizer where the second-order sufficient optimality conditions hold. For a quadratic objective function, a sublinear convergence property is obtained without assuming either nondegeneracy or the second-order sufficient optimality conditions. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • William Hager & Hongchao Zhang, 2014. "An affine scaling method for optimization problems with polyhedral constraints," Computational Optimization and Applications, Springer, vol. 59(1), pages 163-183, October.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:1:p:163-183
    DOI: 10.1007/s10589-013-9535-x
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    References listed on IDEAS

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    1. Paul Tseng, 2004. "Convergence Properties of Dikin’s Affine Scaling Algorithm for Nonconvex Quadratic Minimization," Journal of Global Optimization, Springer, vol. 30(2), pages 285-300, November.
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