On smooth relaxations of obstacle sets
Oliver Stein (steinkit.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
Entry Submitted: 08/18/2011
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