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A First Order Method for Finding Minimal Norm-Like Solutions of Convex Optimization Problems

Amir Beck (becka***at***ie.technion.ac.il)
Shoham Sabach (ssabach***at***tx.technion.ac.il)

Abstract: We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish the convergence of the sequence generated by the algorithm as well as a rate of convergence of the sequence of function values. A portfolio optimization example is given in order to illustrate our results.

Keywords: Convex optimization problems, gradient method, portfolio optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 09/21/2011
Entry Accepted: 09/21/2011
Entry Last Modified: 09/21/2011

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