We address the feasibility of the pair of alternative conic systems of constraints Ax = 0, x \in C, and -A^T y \in C^*, defined by an m by n matrix A and a cone C in the n-dimensional Euclidean space. We reformulate this pair of conic systems as a primal-dual pair of conic programs. … Read more
We obtain a new class of primal affine algorithms for the linearly constrained convex programming. It is constructed from a family of metrics generated the r power, r>=1, of the diagonal iterate vector matrix. We obtain the so called weak convergence. That class contains, as particular cases, the multiplicative Eggermont algorithm for the minimization of … Read more
In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, … Read more
The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and … Read more
We present a primal-dual interior-point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior-point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter rho in the merit function is updated automatically such … Read more
In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point … Read more
In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or … Read more
Interior Point methods for Nonlinear Programming have been extensively used to solve the Optimal Power Flow problem. These optimization algorithms require the solution of a set of nonlinear equations to obtain the optimal solution of the power network equations. During the iterative process to solve these equations, the search for the optimum is based on … Read more
In this paper we study practical solution methods for finding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in $\Re^n$ defined by a finite set of linear inequalities. Our goal is to design a general-purpose algorithmic framework that is reliable and efficient in practice. To evaluate the merit of a practical algorithm, we consider two … Read more
Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \in P, where P is a closed convex set, not necessarily a cone. We bound the complexity of computing an almost-optimal solution of this problem in terms of natural geometry-based measures of the feasible region and the level-set of … Read more