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On the Supremum in Quadratic Fractional Programming
2001We consider the maximization of a ratio f of an arbitrary quadratic function and an affine function over a closed and unbounded set. The behavior of unbounded feasible sequences is studied in order to derive a) conditions under which f attains a finite supremum and b) conditions which guarantee that its supremum is finite.
CAMBINI, ALBERTO +2 more
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Duality for nonlinear fractional programs
Zeitschrift für Operations Research, 1973This paper develops duality results for nonlinear fractional programming problems. This is accomplished by using some known results connecting the solutions of a nonlinear fractional program with those of a suitably defined parametric convex program.
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Parametric approaches to fractional programs
Mathematical Programming, 1983The fractional program P is defined by maxf(x)/g(x) subject tox∈X. A class of methods for solving P is based on the auxiliary problem Q(λ) with a parameter λ: maxf(x)−λg(x) subject tox∈X. Starting with two classical methods in this class, the Newton method and the binary search method, a number of variations are introduced and compared.
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Fractional Programming. I, Duality
Management Science, 1976This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e., maximization of quotients subject to constraints. In Part I a duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector, Craven-Mond, Jagannathan, Sharma-Swarup, et al.
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Markov Renewal Programming by Linear Fractional Programming
SIAM Journal on Applied Mathematics, 1966Markov renewal programming is treated by linear fractional programming. Particular attention is given to the resolution of tied policies that minimize expected cost per unit time. The multichain case is handled by a decomposition approach.
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On Duality for Fractional Programming
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1979Craven, B. D., Mond, B.
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Programming Problems with Convex Fractional Functions
Operations Research, 1968The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of this result and a few applications to mathematical programming are also considered.
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1971
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Fractional Programming Applications
1997The applications of linear programming to various branches of human activity, and especially to economics, are well known. The applications of fractional programming are less known, and, until now, less numerous. Of course, the linearity of a problem makes it easier to tackle, and hence contributes to its wide recognition.
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