We present a new framework for efficiently finding competitive solutions for the facility-layout problem. This framework is based on the combination of two new mathematical-programming models. The first model is a relaxation of the layout problem and is intended to find good starting points for the iterative algorithm used to solve the second model. The … 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
The Fortran subroutine NLPQLP solves smooth nonlinear programming problems and is an extension of the code NLPQL. The new version is specifically tuned to run under distributed systems. A new input parameter l is introduced for the number of parallel machines, that is the number of function calls to be executed simultaneously. In case of … 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 present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally … Read more
Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior … Read more
The authors of this paper recently introduced a transformation \cite{BuMoZh99-1} that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based … Read more
This paper presents and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that either improves the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, … Read more
In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm’s distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X = RR^T. The rank of the factorization, i.e., … Read more