Convex Nondifferentiable Optimization: a Survey Focussed on the Analytic Center Cutting Plane Method
AbstractWe present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant fucntions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts. We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.
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Bibliographic InfoPaper provided by Ecole des Hautes Etudes Commerciales, Universite de Geneve- in its series Papers with number 99.2.
Length: 41 pages
Date of creation: 1999
Date of revision:
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Postal: Suisse; Ecole des Hautes Etudes Commerciales, Universite de Geneve, faculte des SES. 102 Bb. Carl-Vogt CH - 1211 Geneve 4, Suisse
Web page: http://www.hec.unige.ch/
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OPTIMIZATION ; MATHEMATICAL ANALYSIS;
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- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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