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Interior-point methods for convex programming

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Abstract

This work is concerned with generalized convex programming problems, where the objective function and also the constraints belong to a certain class of convex functions. It examines the relationship of two basic conditions used in interior-point methods for generalized convex programming—self-concordance and a relative Lipschitz condition—and gives a short and simple complexity analysis of an interior-point method for generalized convex programming. In generalizing ellipsoidal approximations for the feasible set, it also allows a geometrical interpretation of the analysis.

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Authors and Affiliations

  1. Department of Operations Research, Stanford University, 94305, Stanford, CA, USA

    Florian Jarre

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  1. Florian Jarre
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Communicated by J. Stoer

This work was supported by a research grant from the Deutsche Forschungsgemeinschaft, and in part by the U.S. National Science Foundation Grant DDM-8715153 and the Office of Naval Research Grant N00014-90-J-1242.

On leave from the Institut für Angewandte Mathematik, University of Würzburg, Am Hubland, W-8700 Würzburg, Federal Republic of Germany.

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Jarre, F. Interior-point methods for convex programming. Appl Math Optim 26, 287–311 (1992). https://doi.org/10.1007/BF01371086

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