Journal ArticleDOI
On Nonlinear Fractional Programming
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In this paper, an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator is presented. But the algorithm is based on a theorem by Jagannathan Jagannathy, R. 1966.Abstract:
The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci.12 609--615. concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart.3 71--93. for linear fractional programming and to the quadratic parametric approach by Ritter Ritter, K. 1962. Ein Verfahren zur Losung parameterabhangiger, nichtlinearer Maximum-Probleme. Unternehmensforschung, Band 6, S. 149--166.. The Appendix contains a numerical example.read more
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Practical Non-Linear Energy Harvesting Model and Resource Allocation for SWIPT Systems
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Fractional Programming for Communication Systems—Part I: Power Control and Beamforming
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Optimization Transfer Using Surrogate Objective Functions
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References
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Journal ArticleDOI
Programming with linear fractional functionals
Journal ArticleDOI
On Some Properties of Programming Problems in Parametric form Pertaining to Fractional Programming
TL;DR: This paper presents results which apply to convex programming problem in parametric form and is extended to general non-linear programming problems with special reference to continuous criterion functions.
Journal ArticleDOI
Parametric Objective Function (Part 1)
Thomas L. Saaty,Saul I. Gass +1 more
TL;DR: Using the simplex method, a computational procedure is described which enables one, given a feasible solution, to determine the values of the parameter (if any) for which the solution minimizes the objective function.
Journal ArticleDOI
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.