A superlinearly convergent projection algorithm for solving the convex inequality problem

Authors:
Ubaldo M. GarcıA-Palomares
Affiliations:
Universidad Simón Bolıvar, Departamento de Procesos y Sistemas, Apartado 89000 Caracas 1081-A, Venezuela
Venue:
Operations Research Letters
Year:
1998

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Abstract

The Convex Inequality Problem (CIP), i.e., find x@?R^n such that Ax=b,g(x)=R^m is a convex function, has been solved by projection algorithms possessing a linear rate of convergence. We propose a projection algorithm that exhibits global and superlinear rate of convergence under reasonable assumptions. Convergence is ensured if the CIP is not empty. A direction of search is found by solving a quadratic programming problem (the projection step). As opposed to previous algorithms no special stepsize procedure is necessary to ensure a superlinear rate of convergence. We suggest a possible application of this algorithm for solving convex constrained Linear Complementarity Problems, i.e., find x@?R^n such thatx=0,Ax+b=0,x,Ax+b=0,g(x)=R^m is a convex function.