A parallel algorithm for solving large convex minimax problems

Authors:
Ramnik Arora;Utkarsh Upadhyay;Rupesh Tulshyan;J. Dutta
Affiliations:
The Courant Institute of Mathematical Sciences, New York University;The Department of Computer Science, EPFL, Lausanne;The Department of Mathematics and Statistics, Indian Institute of Technology Kanpur;Indian Institute of Technology Kanpur, Kanpur, India
Venue:
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Year:
2010

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Abstract

We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The algorithm developed estimates the direction of steepest-descent rapidly and using Armijo's condition proceeds towards the solution. Owing to the highly parallel nature of the algorithm, it is highly suitable for large minimax problems. Algorithm is implemented on Nvidia Tesla C1060 graphics card using CUDA and numerical comparisons with RGA & CFSQP are presented.