We extend the analysis of [27] to handling more general utility functions: piece-wise linear functions, which include Leontief’s utility. We show that the problem reduces to the general analytic center model discussed in [27]. Thus, the same linear programming complexity bound applies to approximating the Fisher equilibrium problem with these utilities. More importantly, we show … Read more
We discuss local convergence of Newton’s method to a singular solution $x^*$ of the nonlinear equations $F(x) = 0$, for $F:\R^n \rightarrow \R^n$. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution $x^*$ from a starlike domain around $x^*$ for $F$ twice Lipschitz continuously differentiable and $x^*$ satisfying … Read more
We correct an error in Algorithms 4.1 and 4.8 from the paper with the same title that was published in Optimization Methods and Software, 20, 1 (2005), 145–168. Citationsubmitted to Optimization Methods and SoftwareArticleDownload View PDF
We correct an error in Algorithm 2 from the paper with the same name that was published in Mathematical Programming, Ser. A, 100, 2(2004), 317–337. Citationsubmitted to Mathematical ProgrammingArticleDownload View PDF
Corrector-predictor methods for sufficient linear complementarity problems in a wide neighborhood of the central path CitationTechnical Report UMBC, TR2006-22, January 2005, Revised: March 2006.ArticleDownload View PDF
Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm … Read more
We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for … Read more
In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in \cite{YOSHISE04} for standard form of the problems. We show that the extended model inherits the following desirable features: (a) A path exists, is bounded and has a trivial starting point without any regularity … Read more
We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise … Read more
We consider a regularization proximal method with variable metric to solve the nonlinear complementarity problem (NCP) for P0-functions. We establish global convergence properties when the solution set is non empty and bounded. Furthermore, we prove, without boundedness of the solution set, that the sequence generated by the algorithm is a minimizing sequence for the implicit … Read more