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Adrian S. Lewis(aslewisorie.cornell.edu) Abstract: To minimize or upperbound the value of a function ``robustly'', we might instead minimize or upperbound the ``epsilonrobust regularization'', defined as the map from a point to the maximum value of the function within an epsilonradius. This regularization may be easy to compute: convex quadratics lead to semidefiniterepresentable regularizations, for example, and the spectral radius of a matrix leads to pseudospectral computations. For favorable classes of functions, we show that the robust regularization is Lipschitz around any given point, for all small epsilon > 0, even if the original function is nonlipschitz (like the spectral radius). One such favorable class consists of the semialgebraic functions. Such functions have graphs that are finite unions of sets defined by finitelymany polynomial inequalities, and are commonly encountered in applications. Keywords: robust optimization, nonsmooth analysis, locally Lipschitz, regularization, semialgebraic, pseudospectrum, robust control, semidefinite representable, proxregularity. Category 1: Robust Optimization Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 3: Applications  Science and Engineering (Control Applications ) Citation: Download: [PDF] Entry Submitted: 10/01/2008 Modify/Update this entry  
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