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Convex approximations in stochastic programming by semidefinite programming

István Deák(istvan.deak***at***uni-corvinus.hu)
Imre Pólik(imre***at***polik.net)
András Prékopa(andras.prekopa***at***gmail.com)
Tamás Terlaky(terlaky***at***lehigh.edu)

Abstract: The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in $L_1$, $L_\infty$ and $L_2$ norm. Extensive numerical experiments to investigate the behaviour of the proposed methods are also performed.

Keywords: convex approximation, stochastic optimization, successive regression approximations, semidefinite optimization

Category 1: Stochastic Programming

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 04/20/2010
Entry Accepted: 04/20/2010
Entry Last Modified: 04/20/2010

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