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The Support of Integer Optimal Solutions [PDF]
SIAM Journal on Optimization, 2018 The support of a vector is the number of nonzero-components. We show that given an integral $m\times n$ matrix $A$, the integer linear optimization problem $\max\left\{\boldsymbol{c}^T\boldsymbol{x} : A\boldsymbol{x} = \boldsymbol{b}, \, \boldsymbol{x}\ge\boldsymbol{0}, \,\boldsymbol{x}\in\mathbb{Z}^n\right\}$ has an optimal solution whose support is ...
Iskander Aliev +4 more
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Remarks on the integer Talmud solution for integer bankruptcy problems
Top, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vito Fragnelli
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On the existence of optimal solutions to integer and mixed-integer programming problems
Mathematical Programming, 1974The purpose of this paper is to present sufficient conditions for the existence of optimal solutions to integer and mixed-integer programming problems in the absence of upper bounds on the integer variables. It is shown that (in addition to feasibility and boundedness of the objective function) (1) in the pure integer case a sufficient condition is ...
R R Meyer
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Uniqueness of integer solution of linear equations
Optimization Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Ferris, O L Mangasarian
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Integer Solution for Linear Complementarity Problem
Mathematics of Operations Research, 1998We consider the problem of finding an integer solution to a linear complementarity problem. We introduce the class I of matrices for which the corresponding linear complementarity problem has an integer complementary solution for every vector, q, for which it has a solution.
R. Chandrasekaran +2 more
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Integer solutions to bankruptcy problems with non-integer claims
Top, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vito Fragnelli
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Integer Solution to Synthesis of Communication Networks
Mathematics of Operations Research, 1992This paper describes a polynomial-time algorithm for the following problem: Let ri,j be the given requirements for all i, j ∈ {1, …, n}, with ri,j = rj,i for i, j. Find integer capacities ci,j for all i, j ∈ {1, …, n} such that (considering 1, …, n as the vertices of an undirected network N, with capacities ci,j): (i) for for all i ≠ j there exists a
S. Sridhar, R. Chandrasekaran
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On the Integer Solution of the Transcendental Equation
Indian Journal of Advanced Mathematics, 2022Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation , where 𝒙𝟐−𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.
Sriram S, Veeramallan P
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Watermarking integer linear programming solutions
Proceedings of the 39th conference on Design automation - DAC '02, 2002Linear programming (LP) in its many forms has proven to be an indispensable tool for expressing and solving optimization problems in numerous domains. We propose the first set of generic watermarking techniques for integer-LP (ILP). The proof of authorship by watermarking is achieved by introducing additional constraints to limit the solution space and
Seapahn Megerian +2 more
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Integer Programming Solution of a Classification Problem
Management Science, 1978A classification problem is presented in which it is desired to assign a new individual or observation with k characteristics to one of two distinct populations based upon historical sets of samples from the two populations. The resulting classification problem is formulated as a mixed-integer programming problem.
J. M. Liittschwager, C. Wang
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