Showing papers by "Tamás Terlaky published in 1999"
TL;DR: It is shown that this bound is sharp in order, as far as the dependence on m is concerned, and that a~feasible solution x to (P) with x^TAx\ge \frac{{\Opt(\hbox{{\rm SDP}})}}{{2\ln(2m^2)}} \eqno{(*)}$$ can be found efficiently.
Abstract: We demonstrate that if A1;:::; Am are symmetric positive semidefinite nn matrices with positive definite sum and A is an arbitrary symmetric n n matrix, then the relative accuracy, in terms of the optimal value, of the semidefinite relaxation
195 citations
TL;DR: In this paper, the authors present a complexity analysis of the column generation method in the general semi-infinite case, in terms of the problem dimension, the radius of the largest Euclidean ball contained in the feasible set and the desired accuracy of the approximate solution.
23 citations
TL;DR: In this paper, mixed-integer nonlinear programming (MINLP) is used as the optimization method for determining optimal loading schemes in nuclear reactor fuel management, and it is shown that MINLP combined with local search heuristics is a promising approach to fuel management optimization.
17 citations
TL;DR: This paper will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices based on the principal pivot transform and the orthogonality property of basis tableaus.
Abstract: Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex–based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.
10 citations
TL;DR: In this paper, the finite crisscross method is generalized to solve hyperbolic (fractional linear) programming problems and proved its finiteness under the usual mild assumptions.
10 citations
TL;DR: Several adaptations and model adjustments are described that make the model tractable for a general nonlinear mixed-integer solver to search for optimal fuel loading schemes to solve the nuclear reactor fuel management problem.
Abstract: We use a simpliied but still quite realistic model to the nuclear reactor fuel management problem to search for optimal fuel loading schemes. Several adaptations and model adjustments are described that make the model tractable for a general nonlinear mixed-integer solver. Results are compared with results from pairwise interchange optimization. Use of solutions from nonlinear mixed-integer optimization as starting values for local search heuristics leads to powerful optimization methods.
10 citations
TL;DR: It is shown that Broyden's result straightforwardly follows from well-known theorems of the alternative, like Motzkin's transposition theorem and Tucker's theorem, which are all logically equivalent to Farkas' lemma.
8 citations
TL;DR: In this article, the authors show how to analyze primal-dual affine-scaling methods in the framework of potential reduction algorithms and suggest implementable variants of the methods as long step predictor-corrector (LSPC) algorithms, where the step length is determined by the potential function.
4 citations
TL;DR: In this article, the authors give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow induced by projecting the homogeneous affine scaling vector field conically onto a hyperplane where the objective function is constant.
Abstract: Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail to converge to an optimal solution with the step-size λ=0.999 . In this note, we give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow induced by projecting the homogeneous affine scaling vector field conically onto a hyperplane where the objective function is constant. Based on this interpretation, we show that the algorithm can fail for "any" λ greater than about 0.91 (a more precise value is 0.91071), which is considerably shorter than λ = 0.95 and 0.99 recommended for efficient implementations.
3 citations