Cutting plane methods require the solution of a sequence of linear programs where the solution to one provides a warm start to the next A cutting plane algorithm for solving the linear ordering problem is described This algorithm uses the primal dual interior point method to solve the linear programming relaxations A point which is a good warm start for a simplex based cutting plane algorithm i...

Part II of this study uses the path-following theory of labelled V-complexes developed in Part I to provide constructive algorithmic proofs of a variety of combinatorial lenmas in topology. \Je demonstrate two new dual lemmas on the n-dimensional cube, and use a Generc.lized S ^erner Lemma to prove a gener lization of the Knaster-Kuratowski-y.azurkiewicz Covering Lemma on the simplex. We also s...

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $gamma$-cuts of fuzzy coefficients. Then, we consider a fix $g...

A dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay-o(s is equivalent to a primal-dual pair of such fuzzy linear programming problems. Further certain di6culties with similar studies reported in the literature are discussed.

In fuzzy algebra, fuzzy subspaces are basic concepts. They had been introduced by Katsaras and Liu 1 in 1977 as a generalization of the usual notion of vector spaces. Since then, many results of fuzzy subspaces had been obtained in the literature 1–4 . Moreover, many researches in fuzzy algebra are closely related to fuzzy subspaces, such as fuzzy subalgebras of an associative algebra 5 , fuzzy...

This thesis aims to study the theoretical complexity and empirical performance of decomposition algorithms. We focus on linear programs with a block-angular structure. Decomposition algorithms used to be the only way to solve large-scale special structured problems, in terms of memory limit and CPU time. However, with the advances in computer technology over the past few decades, many large-sca...

Primal-dual pairs of semideenite programs provide a general framework for the theory and algorithms for the trust region subproblem (TRS). This latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and, therefore, it is a generalization of the minimum eigenvalue problem. The importance of (TRS) is due to the fact that it provides the step in...

A dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay-o(s is equivalent to a primal–dual pair of such fuzzy linear programming problems. Further certain di6culties with similar studies reported in the literature are discussed. c © 2003 Elsevier B.V. All rights reserved.

In the field of 3D images, relevant information can be difficult to interpret without further computer-aided processing. Generally, and this is particularly true in medical imaging, a segmentation process is run and coupled with a visualization of the delineated structures. Amongst all techniques based on deformable models, simplex meshes, in particular, present good propensities to handle a la...