Journal Article10.1007/BF01669677
A dual non-linear program
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TL;DR: In this article, a dual of a nonlinear fractional functional programming problem has been formulated, which can be used to obtain a solution of the mixed 0-1 integer linear programming problem.
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Abstract: In the paper a dual of a nonlinear fractional functional programming problem has been formulated. This problem can be used to obtain a solution of the mixed 0–1 integer linear programming problem. Some properties related to the primal and dual have been given.
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Citations
A sixth bibliography of fractional programming
TL;DR: In this article, the authors present a list of 491 papers dealing with fractional programming and its applications, covering mainly the period 1997-2005 but also including some references published up to 1997 which were not included in the previous bibliographies or which were mentioned as ‘to appear’ in the five previous bibliography.
Bibliography in fractional programming
Siegfried Schaible
- 01 Dec 1982
TL;DR: A bibliography in fractional programming is provided which contains 551 references and was attempted to include all publications in this area of nonlinear programming as they have appeared in more than 45 years now.
75
Weber's problem and weiszfeld's algorithm in general spaces
TL;DR: For solving the Euclidean distance Weber problem Weiszfeld proposed an iterative method that can be applied to generalized Weber problems in Banach spaces and Fermat's principle in geometrical optics.
74
Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems
TL;DR: In this paper, necessary and sufficient optimality conditions for a class of constrained variational problems containing arbitary norms are established, and the forms and contents of these optimality results are utilized as a basis for constructing two parametric and eight parameter-free duality models and proving appropriate duality theroems.
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References
A duality theorem for non-linear programming
TL;DR: In this paper, a dual problem for the mathematical programming problem of minimizing a convex function under convex constraints was formulated, which reduces to the classical dual problem in the case of linear programming problems.
The Direct Power of Adjacent Vertex Programming Methods
TL;DR: In this paper, the power of adjacent vertex methods in solving non-linear programming problems is investigated, restricted to variables and objective functions which are continuous and exclude any transformation or approximation of the original system.
94
Duality in homogeneous programming
E Eisenberg
- 26 Jun 1961
TL;DR: In this article, it was shown that the problem of maximizing a concave function subject to linear constraints does not have a dual, as is the case in linear programming, in which primal optimizing variables do not appear.
Symposium on Modern Techniques for Extremum Problems—Linear and Nonlinear Programming
TL;DR: In this article, the linear programming problem of minimizing a linear objective function subject to linear constraints (inequalities and/or equations, some variables nonnegative) is embedded in the larger problem of minimization of a convex objective subject to such linear constraints.
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