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A first-order interior-point method for linearly constrained smooth optimization

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Abstract

We propose a first-order interior-point method for linearly constrained smooth optimization that unifies and extends first-order affine-scaling method and replicator dynamics method for standard quadratic programming. Global convergence and, in the case of quadratic program, (sub)linear convergence rate and iterate convergence results are derived. Numerical experience on simplex constrained problems with 1000 variables is reported.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Paul Tseng

  2. Department of Statistics and Decision Support Systems, University of Vienna, Brünnerstr. 72, 1210, Vienna, Austria

    Immanuel M. Bomze & Werner Schachinger

Authors
  1. Paul Tseng
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  2. Immanuel M. Bomze
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  3. Werner Schachinger
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Correspondence to Paul Tseng.

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Tseng, P., Bomze, I.M. & Schachinger, W. A first-order interior-point method for linearly constrained smooth optimization. Math. Program. 127, 399–424 (2011). https://doi.org/10.1007/s10107-009-0292-7

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  • DOI: https://doi.org/10.1007/s10107-009-0292-7

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