Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interior-point type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems that also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for large-scale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Department of Management, Odense University, Campusvej 55, DK-5230 Odense M, Denmark. E-mail: eda@busieco.ou.dk y ...

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In this study, we propose a novel optimization algorithm for minimum classification error (MCE) training of modified quadratic discriminant function (MQDF) models. An ellipsoid constrained quadratic programming (ECQP) problem is formulated with an efficient line search solution derived, and a subspace combination condition is proposed to simplify the problem in certain cases. We show that under the perspective of constrained optimization, the MCE training of MQDF models can be solved by ECQP with some reasonable approximation, and the hurdle of incomplete covariances can be handled by subspace combination. Experimental results on the Nakayosi/Kuchibue online handwritten Kanji character recognition task show that compared with the conventional generalized probabilistic descent (GPD) algorithm, the new approach achieves about 7 % relative error rate reduction. 1.