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Exact penalty and error bounds in DC programming

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Abstract

In the present paper, we are concerned with conditions ensuring the exact penalty for nonconvex programming. Firstly, we consider problems with concave objective and constraints. Secondly, we establish various results on error bounds for systems of DC inequalities and exact penalty, with/without error bounds, in DC programming. They permit to recast several class of difficult nonconvex programs into suitable DC programs to be tackled by the efficient DCA.

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Authors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science—LITA EA 3097, UFR MIM, University of Paul Verlaine—Metz, Ile du Saulcy, 57045, Metz, France

    Hoai An Le Thi

  2. LMI-National Institute for Applied Sciences-Rouen, BP08-Avenue de l’Université, 76801, Saint-Etienne-du-Rouvray, France

    Tao Pham Dinh

  3. Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

    Huynh Van Ngai

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  1. Hoai An Le Thi
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  2. Tao Pham Dinh
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  3. Huynh Van Ngai
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Correspondence to Hoai An Le Thi.

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The paper is dedicated to the memory of our friend Reiner Horst.

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Le Thi, H.A., Pham Dinh, T. & Ngai, H.V. Exact penalty and error bounds in DC programming. J Glob Optim 52, 509–535 (2012). https://doi.org/10.1007/s10898-011-9765-3

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