Results 131 to 140 of about 750,593 (188)

Solving linear programming problems via linear minimax problems

Applied Mathematics and Computation, 1991
The linear programming problem consists of minimizing \(c^ Tx\) subject to \(A^ Tx\geq b\) where \(x\in \mathbb{R}^ n\) is variable, \(c\in \mathbb{R}^ n\), \(b\in \mathbb{R}^ n\) are given, and \(A\) is an \(n\times m\) matrix which is also given.
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LINEAR PROGRAMMING CUTTING PROBLEMS

International Journal of Software Engineering and Knowledge Engineering, 1993
Different optimal cutting problems are considered in this paper. Among them are cutting forming problems (closed packing problems) and problems of cutting totality planning with intensities of their application. For solving these planning problems, linear or integer programming is used.
E.A. MUKHACHIOVA, V.A. ZALGALLER
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The Linear Programming Problem

2001
Linear 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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Linear Interval Tolerance Problem and Linear Programming Techniques

Reliable Computing, 2001
Let \([A]x= [b]\) 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.
Beaumont, Oliver, Philippe, Bernard
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Linear Optimal Control Problems and Generalized Linear Programs

Journal of the Operational Research Society, 1981
Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state constraints.
Dantzig, G. B., Sethi, S. P.
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Generating Linear and Linear-Quadratic Bilevel Programming Problems

SIAM Journal on Scientific Computing, 1993
This paper proposes a method for generating linear and linear-quadratic bilevel programming problems. This is useful for generating test problems. In particular, the proposed technique allows for the generation of test problems with various pre-determined characteristics (e.g., the number and type of minima).
Calamai, Paul H., Vicente, Luis N.
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Minimax linear programming problem

Operations Research Letters, 1985
The author is concerned with the following minimax problem; \[ (MLPP)\quad \min z=\max_{1\leq j\leq n}\{c_ jx_ j\}\quad subject\quad to\quad Ax=g,\quad x\geq 0 \] where \(c_ j\geq 0\) and \(x_ j\) are scalars, x is a column vector with components \(x_ j\), g is a column vector with elements \(g_ j\geq 0\) and A is a \(m\times n\) matrix of rank m.
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Linear Programming. Transportation Problem

2009
The problem to find a vector x *= (x * 1, x * 2,…, x * n)Tsuch that its components satisfy the conditions.
Bernd Luderer, Volker Nollau, Klaus Vetters   +2 more
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Converting Linear Programs to Network Problems

Mathematics of Operations Research, 1980
We describe an algorithm which converts a linear program min{cx ∣ Ax = b, x ≥ 0} to a network flow problem, using elementary row operations and nonzero variable-scaling, or shows that such a conversion is impossible. If A is in standard form, the computational effort required is bounded by O(rn), where r is the number of rows and n is the number of ...
Bixby, Robert E., Cunningham, William H.
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