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On smooth relaxations of obstacle sets

Oliver Stein (stein***at***kit.edu)
Paul Steuermann (steuermann***at***kit.edu)

Abstract: We present and discuss a method to relax sets described by finitely many smooth convex inequality constraints by the level set of a single smooth convex inequality constraint. Based on error bounds and Lipschitz continuity, special attention is paid to the maximal approximation error and a guaranteed safety margin. Our results allow to safely avoid the obstacle by obeying a single smooth constraint. Numerical results indicate that our technique gives rise to a smoothing method which performs well even for smoothing parameters very close to zero.

Keywords: Relaxation, error bound, Lipschitz continuity, hyperbolic smoothing, entropic smoothing, obstacle problem.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Optimization and Engineering, online first, DOI 10.1007/s11081-013-9224-8

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Entry Submitted: 08/18/2011
Entry Accepted: 08/18/2011
Entry Last Modified: 06/11/2013

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