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Interior Point Methods for Second-Order Cone Programming and OR Applications

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Abstract

Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an affine set. It is described in detail how to convert several application problems to SOCP. Moreover, a proof is given of the existence of the step for the infeasible long-step path-following method. Furthermore, variants are developed of both long-step path-following and of predictor-corrector algorithms. Numerical results are presented and analyzed for those variants using test cases obtained from a number of application problems.

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Authors and Affiliations

  1. Mathematics Department, Indiana University of Pennsylvania, Indiana, PA, 15705, USA

    Yu-Ju Kuo

  2. Department of Mathematics & Statistics, Arizona State University, Tempe, AZ, 85287-1804, USA

    Hans D. Mittelmann

Authors
  1. Yu-Ju Kuo
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  2. Hans D. Mittelmann
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Kuo, YJ., Mittelmann, H.D. Interior Point Methods for Second-Order Cone Programming and OR Applications. Computational Optimization and Applications 28, 255–285 (2004). https://doi.org/10.1023/B:COAP.0000033964.95511.23

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  • DOI: https://doi.org/10.1023/B:COAP.0000033964.95511.23

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