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Zbl 1065.90060
Goffin, Jean-Louis; Vial, Jean-Philippe
Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method. (English)
[J] Optim. Methods Softw. 17, No. 5, 805-867 (2002). ISSN 1055-6788; ISSN 1029-4937/e

Summary: 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 functions, 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.

MSC 2000:: *90C25 Convex programming
49J52 Nonsmooth analysis (other weak concepts of optimality)
90-02 Research monographs (optimization)
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut

Keywords: Nondifferentiable Optimization; Analytic Center; Cutting Plane Methods

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