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Exact regularization of convex programs

Michael Friedlander
Computer Science, University of British Columbia


An optimization problem is ill-posed if its solution is not unique oris acutely sensitive to data perturbations. A common approach to suchproblems is to construct a related problem with a well-behavedsolution that deviates only slightly from the original solution set.The strategy is often used in data fitting applications, and alsowithin optimization algorithms as a means for stabilizing the solutionprocess.

This approach is known as regularization, and deviations fromsolutions of the original problem are generally accepted as atrade-off for obtaining solutions with other desirable properties.

In fact, however, there exist necessary and sufficient conditions suchthat solutions of the regularized problem continue to be exactsolutions of the original problem. We present these conditions forgeneral convex programs, and give some applications of exactregularization.

(Joint work with Paul Tseng.)

Thursday, June 7, 2007
2:00PM AP&M 6402