Randomized Search Directions in Descent Methods for Minimizing Certain Quasi-Differentiable Functions

Kiwiel, K. (1984). Randomized Search Directions in Descent Methods for Minimizing Certain Quasi-Differentiable Functions. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-056

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Abstract

Several descent methods have recently been proposed for minimizing smooth compositions of max-type functions. The methods generate many search directions at each iteration. It is shown here that a random choice of only two search directions at each iteration suffices to retain convergence to in#-stationary points with probability 1. Use of this technique may significantly decrease the effort involved in quadratic programming and line searches, thus allowing efficient implementations of the methods.

This paper is a contribution to research on non-smooth optimization currently underway in the System and Decision Sciences Program.

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