A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization

Authors:
Erling D. Andersen;Yinyu Ye
Affiliations:
Department of Management, Odense University, Campusvej 55, DK-5230 Odense M, Denmark. E-mail: eda@busieco.ou.dk;Department of Management Sciences, The University of Iowa, Iowa City, Iowa 52242, USA. E-mail: yyye@dollar.biz.uiowa.edu
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

Recently the authors have proposed a homogeneous and self-dualalgorithm for solving the monotone complementarity problem (MCP) [5]. Thealgorithm is a single phase interior-point type method; nevertheless, ityields either an approximate optimal solution or detects a possibleinfeasibility of the problem. In this paper we specialize the algorithm tothe solution of general smooth convex optimization problems, which also possess nonlinear inequality constraints and free variables. We discuss animplementation of the algorithm for large-scale sparse convex optimization.Moreover, we present computational results for solving quadraticallyconstrained quadratic programming and geometric programming problems, wheresome of the problems contain more than 100,000 constraints and variables.The results indicate that the proposed algorithm is also practicallyefficient.