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Robust regularization

Adrian Lewis (aslewis***at***sfu.ca)

Abstract: Given a real function on a Euclidean space, we consider its "robust regularization": the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint against unpredictable perturbations in variables or data. After outlining some examples, we consider in particular a function that is locally Lipschitz on the complement of a suitably well-behaved (for example, semi- algebraic or prox-regular) small set, and satisfies a growth condition near the set. We show that, around any given point, the robust regularization is eventually locally Lipschitz once the size of the neighbourhood is sufficiently small. Our result applies in particular to the pseudospectral abscissa of a square matrix, a useful function in robust stability theory.

Keywords: robust optimization, nonsmooth analysis, locally Lipschitz, regularization, semi-algebraic, pseudospectrum, robust control, semidefinite representable, prox-regularity

Category 1: Robust Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Applications -- Science and Engineering (Control Applications )

Citation: Technical report, Simon Fraser University, September 2002

Download: [Postscript]

Entry Submitted: 09/19/2002
Entry Accepted: 09/23/2002
Entry Last Modified: 09/23/2002

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