In our reports on GAMM-04 and ECCOMAS-04 there has been presented a new conjugate directions method for large scale unconstrained minimization problems. High efficiency of this method is ensured by employing an orthogonalization procedure: when constructing the next conjugate vector the component of the gradient is used that is orthogonal to the subspace of preceding … Read more
In this report, we propose a new partitioned variable metric method for minimization of nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new … Read more
Employing the variational approach having the two-body reduced density matrix (RDM) as variables to compute the ground state energies of atomic-molecular systems has been a long time dream in electronic structure theory in chemical physics/physical chemistry. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual … Read more
For a real world problem — transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand — we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost … Read more
OOPS is an object oriented parallel solver using the primal dual interior point methods. Its main component is an object-oriented linear algebra library designed to exploit nested block structure that is often present is truly large-scale optimization problems. This is achieved by treating the building blocks of the structured matrices as objects, that can use … Read more
Trust-region methods are very convenient in connection with the Newton method for unconstrained optimization. The More-Sorensen direct method and the Steihaug-Toint iterative method are most commonly used for solving trust-region subproblems. We propose a method which combines both of these approaches. Using the small-size Lanczos matrix, we apply the More-Sorensen method to a small-size trust-region … Read more
In this paper we present a modified nearly exact (MNE) method for solving low-rank trust region (LRTR) subproblem. The LRTR subproblem is to minimize a quadratic function, whose Hessian is a positive diagonal matrix plus explicit low-rank update, subject to a Dikin-type ellipsoidal constraint, whose scaling matrix is positive definite and has the similar structure … Read more
A method for solving inequality constrained minimization problems is described. The algorithm is based on a primal-dual interior point approach, with a line search globalization strategy. A quasi-Newton technique (BFGS) with limited memory storage is used to approximate the second derivatives of the functions. The method is especially intended for solving problems with a large … Read more
Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … 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. CitationSIAG/Opt Views-and-News, Volume 14 Number 1, April 2003. http://fewcal.uvt.nl/sturm/siagopt/ArticleDownload View PDF