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Models and Algorithms for Distributionally Robust Least Squares Problems

Sanjay Mehrotra(mehrotra***at***iems.northwestern.edu)
He Zhang(hezhang2012***at***u.northwestern.edu)

Abstract: We present different robust frameworks using probabilistic ambiguity descriptions of the input data in the least squares problems. The three probability ambiguity descriptions are given by: (1) confidence interval over the first two moments; (2) bounds on the probability measure with moments constraints; (3) confidence interval over the probability measure by using the Kantorovich probability distance. For these three cases we derive equivalent formulations and show that the resulting optimization problem can be solved efficiently.

Keywords: Robust Optimization, Least Squares, Semidefinite Programming

Category 1: Robust Optimization

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 02/15/2011
Entry Accepted: 02/15/2011
Entry Last Modified: 02/15/2011

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