Nicholas I. M. Gould A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, … Read more
A new initialization or `Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path … Read more
The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27–48, 2004). Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic … Read more
In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommanded ranges of values for these parameters are … Read more
A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer and Toint (SIAM J. Optim., to appear 2004) for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algorithm is … Read more
A mixed interior/exterior-point method for nonlinear programming is described, that handles constraints by an L1-penalty function. A suitable decomposition of the penalty terms and embedding of the problem into a higher-dimensional setting leads to an equivalent, surprisingly regular, reformulation as a smooth penalty problem only involving inequality constraints. The resulting problem may then be tackled … Read more
SIAM’s SIAG/Opt Newsletter special issue on Large Scale Nonconvex Optimization. Guest editors Sven Leyffer and Jorge Nocedal, with contributions by Gould, Sachs, Biegler, Waechter, Leyffer, Bussieck and Pruessner. Citation SIAG/Opt Views-and-News, Volume 14 Number 1, April 2003. http://fewcal.uvt.nl/sturm/siagopt/ Article Download View SIAG/Opt Views-and-News Vol 14 No 1
We analyze the global convergence properties of a class of penalty methods for nonlinear programming. These methods include successive linear programming approaches, and more specifically the SLP-EQP approach presented in \cite{ByrdGoulNoceWalt02}. Every iteration requires the solution of two trust region subproblems involving linear and quadratic models, respectively. The interaction between the trust regions of these … Read more
This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained … Read more
The initial release of CUTE, a widely used testing environment for optimization software was described by Bongartz, Conn, Gould and Toint. The latest version, now known as CUTEr, is presented. New features include reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and … Read more