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Outer Approximation Method Incorporating a Quadratic Approximation for a DC Programming Problem

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Abstract

In this paper, we propose an outer approximation method using two quadratic functions approximating the constraint functions of a DC programming problem. By analyzing the relation among the eigenvectors of the Hessian matrices of the constraint functions, the search direction for a feasible solution of the problem is determined. Moreover, to avoid line searches along similar directions, we incorporate a penalty function method in the algorithm.

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Authors and Affiliations

  1. Graduate School of Science and Technology, Niigata University, Niigata, Japan

    S. Yamada & T. Tanaka

  2. Graduate School of Engineering, Osaka University, Osaka, Japan

    T. Tanino

Authors
  1. S. Yamada
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  2. T. Tanaka
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  3. T. Tanino
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Corresponding author

Correspondence to S. Yamada.

Additional information

Communicated by P.M. Pardalos.

The authors are grateful to Professor Panos Pardalos and the anonymous referees for their suggestions on improving of the paper. This work is based on Project 21540121 supported by Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science.

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Yamada, S., Tanaka, T. & Tanino, T. Outer Approximation Method Incorporating a Quadratic Approximation for a DC Programming Problem. J Optim Theory Appl 144, 156–183 (2010). https://doi.org/10.1007/s10957-009-9590-8

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  • DOI: https://doi.org/10.1007/s10957-009-9590-8

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