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DNA solution of integer linear programming
Applied Mathematics and Computation, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shiying Wang, Aimin Yang
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The solution of an integer quadratic programming problem
USSR Computational Mathematics and Mathematical Physics, 1966Abstract In [1] the problem of integer quadratic programming is examined. We consider below a special case of this problem and construct another algorithm for finding an approximate solution. We give the conditions under which the approximate solution is exact.
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On the greedy solution in integer linear programming
Zeitschrift f�r Operations Research, 1987The author generalizes a result of \textit{M. J. Magazine, G. L. Nemhauser} and \textit{L. E. Trotter} jun. [Oper. Res. 23, 207--217 (1975; Zbl 0305.90039)] from knapsack problems to arbitrary integer programs. He states a greedy method for integer programs based on the natural partial order in \(\mathbb R^ n\) and characterizes a class of problems for
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Visual Solution of Integer Optimization Problems
2002There is an objective contradiction between the allowable amount of computer researches and the feasibility of getting the optimal result in mathematical integer programming problems. The visual technique is proposed to settle this contradiction by means of the direct user participation in computer researches.
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A DIOPHANTINE EQUATION AND ITS POSITIVE INTEGER SOLUTIONS
JP Journal of Algebra, Number Theory and Applications, 2022Summary: In 2017, the Diophantine equation (*) \(\frac1x + \frac1y + \frac1z = \frac1{3p}\) was preliminarily discussed in [the author and \textit{Jiagui Luo}, AIMS Math. 2, No. 1, 111--127 (2017; Zbl 1425.11061)]. The positive integer solutions of some equations derived from (*) were solved, where \(p= 661\). In this paper, the equation (*) is further
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Integer Solutions to Linear Equations
1984Consider the system of linear algebraic equations Ax = b, where A is an m x n integer matrix and b is an m-vector with integer components. In general, the solution vector will not necessarily have integer components. However, there are many situations in which we seek an integer solution to such a system.
R. T. Gregory, E. V. Krishnamurthy
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An Integer Programming Problem with a Linear Programming Solution
The American Mathematical Monthly, 20001995. 12. Paul Halmos and Steven Givant, Logic as Algebra, Dolciani Mathematical Expositions-No. 21, The Mathematical Association of America, Washington, D.C., 1998. 13. I. N. Herstein, Topics in Algebra, Xerox College Publishing, Lexington, Mass., 1964 (also: Wiley, New York, 1975). 14.
Kevin A. Broughan, Nan Zhu
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Solution of Integer Programs with a Quadratic Objective Function
Journal of the ACM, 1976This paper presents a branch and bound method for solving problems in which the objective function is quadratic, the constraints are linear, and some or all variables are required to be integer. The algorithm is obtained by grafting an inverse-basis version of Beale's method onto the Land-Doig procedure.
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A heuristic solution procedure for multicommodity integer flows
Computers & Operations Research, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. K. Aggarwal +2 more
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On integer solutions of an arctan problem
International Journal of Mathematical Education in Science and Technology, 2008A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.
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