A center of a polytope: An expository review and a parallel implementation.
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Displaying 1 – 20 of 425
A certified reduced basis method for parametrized elliptic optimal control problems
Mark Kärcher, Martin A. Grepl (2014)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...
A class of combinatorial problems with polynomially solvable large scale set covering/partitioning relaxations
M. Minoux (1987)
RAIRO - Operations Research - Recherche Opérationnelle
A class of nonmonotone stabilization methods in unconstrained optimization.
L. Grippo, F. Lampariello, S. Lucidi (1991)
Numerische Mathematik
A compact variable metric algorithm for linearly constrained nonlinear minimax approximation
Ladislav Lukšan (1985)
Kybernetika
A computational approach to pivot selection in the LP relaxation of set problems.
Djannaty, F., Rostamy, B. (2006)
Journal of Applied Mathematics and Decision Sciences
A conception of optimality for algorithms and its application to the optimal search for a minimum
A. Adamski, A. Korytowski, W. Mitkowski (1977)
Applicationes Mathematicae
A conjugate direction method for approximating the analytic center of a polytope.
Kojima, Masakazu, Megiddo, Nimrod, Mizuno, Shinji (1998)
Journal of Inequalities and Applications [electronic only]
A conjugate gradient method with quasi-Newton approximation
Jonas Koko (2000)
Applicationes Mathematicae
The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
A conjugate gradient method with sufficient descent and global convergence for unconstrained nonlinear optimization.
Liu, Hailin, Cheng, Sui Sun, Li, Xiaoyong (2011)
Applied Mathematics E-Notes [electronic only]
A Constraint Linearization Method for Nondifferentiable Convex Minimization.
Krzysztof C. Kiwiel (1987)
Numerische Mathematik
A contribution to Balas' algorithm
Jaroslav Hrouda (1971)
Aplikace matematiky
A convergence proof of a special version of the generalized reduced gradient method (GRGS)
Yves Smeers (1974)
RAIRO - Operations Research - Recherche Opérationnelle
A convergent algorithm for solving linear programs with an additional reverse convex constraint
Lê Dung Muu (1985)
Kybernetika
A Counterexample to Greenberg's Algorithm for Solving Linear Inequalities.
B.F. Sherman (1976/1977)
Numerische Mathematik
A Cyclic Projection Algorithm Via Duality.
N. Gaffke, R. Mathar (1989)
Metrika
A Decomposition-Dualization Approach for Solving Constraint Convex Minimization Problems with Applications to Discretized Obstacle Problems.
Michael Krätzschmar (1989)
Numerische Mathematik
A dual algorithm for the minimal cost flow problem
Veira Martins, Ernesto Q. (1979)
Portugaliae mathematica
A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing Subsequent Data Changes.
J. Stoer, K. Schittkowski (1978/1979)
Numerische Mathematik
A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures
Kjetil K. Haugen, Guillaume Lanquepin-Chesnais, Asmund Olstad (2012)
Kybernetika
In this paper, we demonstrate the computational consequences of making a simple assumption on production cost structures in capacitated lot-size problems. Our results indicate that our cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable. Our experiments indicate that problems with more than 1000 products in more than 1000 time periods may be solved within reasonable time. The Lagrangian decomposition algorithm we use does of course not...
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