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Convex Nondifferentiable Optimization: a Survey Focussed on the Analytic Center Cutting Plane Method

Author

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  • Goffin, J.-L.
  • Vial, J.-P.

Abstract

We 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.

Suggested Citation

  • Goffin, J.-L. & Vial, J.-P., 1999. "Convex Nondifferentiable Optimization: a Survey Focussed on the Analytic Center Cutting Plane Method," Papers 99.2, Ecole des Hautes Etudes Commerciales, Universite de Geneve-.
    • Handle: RePEc:fth:ehecge:99.2
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    Keywords

    OPTIMIZATION ; MATHEMATICAL ANALYSIS;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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