A Existence Theorem and a Error Bound of the Numerical Solution of Optimization Problems Utilizing the Interior-Point Method

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  • ITOH Teruo
    Faculty of Engineering, Kyushu Institute of Technology
  • TAKATA Sigeo
    Faculty of Engineering, Kyushu Institute of Technology

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  • 内点法を利用した最適化問題の解の存在定理と数値解の誤差範囲
  • ナイテンホウ オ リヨウシタ サイテキカ モンダイ ノ カイ ノ ソンザイ テ

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Abstract

For optimization methods, penalty methods are conventional, although they are approximate methods theoretically. Futhermore the numerical solution is the solution which satisfies the necessarly conditions approximately. So it is important to show the existence of the solution and, if it exists, the error between the numerical solution and the theoretical extremal.<br>In this paper, the theorem is represented, with which any numerical solution can be assured of having an extremal, utilizing the interiror-point method or barrier function method. At the same time, this theorem can give the error bound of the numerical solution from the extremal. The author gave the same theorem utilizing the exterior-point method already. Thus any numerical solution can be assured of the existence of the extremal, if the solution satisfies either the conditions of the theorem in this paper or the conditions of the theorem utilizing the exterior-point method. An illustrative example is given.

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