We consider two standard philosophies for finding minimizing solutions of convex objective functions affected by uncertainty. In a first approach, the solution should minimize the expected value of the objective w.r.t. uncertainty (average approach), while in a second one it should minimize the worst-case objective (worst-case, or min-max approach). Both approaches are however numerically hard to solve exactly, for general dependence of the cost function on the uncertain data. Here, we discuss two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. A specific application to uncertain Least-Squares problems is also examined in the paper.

Average and worst-case techniques in convexoptimization with stochastic uncertainty / Calafiore, Giuseppe Carlo; F., Dabbene. - STAMPA. - (2006), pp. 6614-6619. (Intervento presentato al convegno Joint 44th IEEE Conference on Decision and Control and European Control Conference tenutosi a Seville (Spain) nel 2-15 Dec. 2005) [10.1109/CDC.2005.1583224].

Average and worst-case techniques in convexoptimization with stochastic uncertainty

CALAFIORE, Giuseppe Carlo;
2006

Abstract

We consider two standard philosophies for finding minimizing solutions of convex objective functions affected by uncertainty. In a first approach, the solution should minimize the expected value of the objective w.r.t. uncertainty (average approach), while in a second one it should minimize the worst-case objective (worst-case, or min-max approach). Both approaches are however numerically hard to solve exactly, for general dependence of the cost function on the uncertain data. Here, we discuss two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. A specific application to uncertain Least-Squares problems is also examined in the paper.
2006
0780395670
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1409006
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