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Linear Interval Tolerance Problem and Linear Programming Techniques
Reliable Computing, 2001Let \([A]x= [b]\) be an \(n\)-dimensional system of linear interval equations. Then \(\Sigma_{\forall\exists}\) denotes the set of all \(x\in\mathbb{R}^n\) such that to any \(A\in [A]\) there exists a \(b\in [b]\) with \(Ax= b\). Two different subsets, \(S_1\) and \(S_2\) of \(\Sigma_{\forall\exists}\) which were defined by \textit{J.
Olivier Beaumont, Bernard Philippe
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On solving a D.C. programming problem by a sequence of linear programs
Journal of Global Optimization, 1991Consider the problem of finding the global minimum of the difference of two convex functions over a closed convex set in \(R^ n\), that is \[ \text{glob }\min(f(x)-g(x))\quad\text{s.t. } h_ j(x)\leq 0\;(j=1,\dots,J),\tag{P} \] where \(f\), \(g\), \(h_ j\) are finite convex functions on \(R^ n\). Problem (P) is usually called a d.c. optimization problem
Reiner Horst +3 more
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A Code for the Transportation Problem of Linear Programming
Journal of the ACM, 1976Methods are described and results presented for greatly reducing the computation time for long narrow problems of the transportation problem of linear programming. The code builds on known methods with two principal innovations: a substantial reduction in the size of the tree representation of shipments, and a set of methods for calculating improved ...
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The Linear Programming Problem
2001Linear programming is the problem of optimizing a linear function subject to finitely many linear constraints in finitely many variables. The standard form of the linear programming problem is $$ \min \left\{ {cx:Ax = b,x \geqslant 0} \right\} $$ for data c e ℝn, A ℝmxn and b e ℝm satisfying that the rank of A equals its row rank, i.e., r(A) = m,
Dimitres Alevras, Manfred W. Padberg
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A linear two-level programming problem
Computers & Operations Research, 1982Multi-level programming, as defined in this paper, refers to a problem situation wherein outer decision makers affect the solution space of inner decision makers within a strictly hierarchical structure. The problem corresponds to a primordial economic policy problem since: (i) higher level decision makers have direct control of some variables (the ...
Wilfred Candler, Robert Townsley
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A Linear Programming Formulation of the Problem of Moments
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1979AbstractSolutions of the moment problem are sought in the class of density functions that possess certain conditions of continuity and differentiability. One can accomplish this by the methods of linear optimization if the nodal quantities, for instance, the ordinates and derivatives are retained as independent variables and if the density function is ...
Siu, W. W. C. +2 more
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Generation of Degenerate Linear Programming Problems
Journal of Optimization Theory and Applications, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solving matching problems with linear programming
Mathematical Programming, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grötschel, Martin, Holland, Olaf
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On degeneracy in linear programming and related problems
Annals of Operations Research, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karen George, Michael R. Osborne
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The Linear Programming Problem
2003In verbal terms, the linear programming problem (also referred to as linear program, LP) is to optimize (minimize or maximize) a linear function subject to linear equality and/or inequality constraints.
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