Minimax fractional programming problems are analyzed from the view-point of lower subdifferentiability, obtaining Kuhn-Tucker type optimality conditions. Multiobjective optimization problems with fractional objectives...
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We consider the problem of minimizing the sum of a convex function and of p greater than or equal to 1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the de...
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We consider the problem of minimizing the sum of a convex function and of p greater than or equal to 1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem is NP-complete even when only p = 1 fraction is involved. We then show how the problem can be reduced to the minimization of a function of p variables where the function values are given by the solution of certain convex subproblems. Based on this reduction, we propose an algorithm for computing the global minimum of the problem by means of an interior-point method for convex programs.
We present an algorithm for finding a minimum spanning tree where the costs are the sum of two linear ratios. We show how upper and lower bounds may be quickly generated. By associating each ratio value with a new var...
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We present an algorithm for finding a minimum spanning tree where the costs are the sum of two linear ratios. We show how upper and lower bounds may be quickly generated. By associating each ratio value with a new variable in 'image space,' we show how to tighten these bounds by optimally solving a sequence of constrained minimum spanning tree problems. The resulting iterative algorithm then finds the globally optimal solution. Two procedures are presented to speed up the basic algorithm. One relies on the structure of the problem to find a locally optimal solution while the other is independent of the problem structure. Both are shown to be effective in reducing the computational effort. Numerical results are presented.
In this paper, we will develop an algorithm for solving a quadratic fractional programming problem which was recently introduced by Lo and MacKinlay to construct a maximal predictability portfolio, a new approach in p...
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In this paper, we will develop an algorithm for solving a quadratic fractional programming problem which was recently introduced by Lo and MacKinlay to construct a maximal predictability portfolio, a new approach in portfolio analysis. The objective function of this problem is defined by the ratio of two convex quadratic functions, which is a typical global optimization problem with multiple local optima. We will show that a well-designed branch-and-bound algorithm using (i) Dinkelbach's parametric strategy, (ii) linear overestimating function and (iii) omega -subdivision strategy can solve problems of practical size in an efficient way. This algorithm is particularly efficient for Lo-MacKinlay's problem where the associated nonconvex quadratic programming problem has low rank nonconcave property.
This paper studies a bicriteria integer nonlinear fractional programming problem. An integer nonlinear fractional programming problem with one of the objective functions as the principal objective is considered. An in...
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This paper studies a bicriteria integer nonlinear fractional programming problem. An integer nonlinear fractional programming problem with one of the objective functions as the principal objective is considered. An integer linear fractional programming problem related to this is constructed. By varying the minimum acceptable values of the second level objective a sequence of the constrained integer nonlinear fractional programming problems is solved to generate the exhaustive set of efficient solutions. Ranking of integer solutions of the linear fractional programming problem helps in finding the optimal integer solutions of the sequence of constrained nonlinear fractional programming problems.
A class-dependent weighted (CDW) dissimilarity measure in vector spaces is proposed to improve the performance of the nearest neighbor (NN) classifier. In order to optimize the required weights, an approach based on F...
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A class-dependent weighted (CDW) dissimilarity measure in vector spaces is proposed to improve the performance of the nearest neighbor (NN) classifier. In order to optimize the required weights, an approach based on fractional programming is presented. Experiments with several standard benchmark data sets show the effectiveness of the proposed technique. (C) 2000 Published by Elsevier Science B.V.
Based on an approach recently proposed for obtaining global optimal solution of general 0-1 fractional programming (G-FP) problem, a theorem is presented in this research. Through this theorem, the nonlinear terms app...
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Based on an approach recently proposed for obtaining global optimal solution of general 0-1 fractional programming (G-FP) problem, a theorem is presented in this research. Through this theorem, the nonlinear terms appearing in the formulation transformed from G-FP can be directly replaced by a set of linear inequalities. The G-FP problem can hence be easily and more efficiently solved as a mixed integer program. (C) 1997 Elsevier Science B.V.
In this paper we adapt the well-known parametric approach from fractional programming to solve a class of fractional programs with a noncompact feasible region. Such fractional problems belong to an important class of...
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In this paper we adapt the well-known parametric approach from fractional programming to solve a class of fractional programs with a noncompact feasible region. Such fractional problems belong to an important class of single component preventive maintenance models. Moreover, for a special but important subclass we show that the subproblems occurring in this parametric approach are easy solvable. To solve the problem directly we also propose for a related subclass a specialized version of the bisection method. Finally, we present some computational results for these two methods applied to an inspection model and a minimal repair model having both a unimodal failure rate.
This short note revisits an algorithm previously sketched by Mathis and Mathis [SIAM Rev., 37 (1995), pp. 230-234] and used to solve a nonlinear hospital fee optimization problem. An analysis of the problem structure ...
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This short note revisits an algorithm previously sketched by Mathis and Mathis [SIAM Rev., 37 (1995), pp. 230-234] and used to solve a nonlinear hospital fee optimization problem. An analysis of the problem structure reveals how the Simplex algorithm, viewed under the correct light, can be the driving force behind a successful algorithm for an almost linear problem. This presentation is intended for students who have been exposed to the Simplex method for linear programming and are progressing, via the Karush-Kuhn-Tucker conditions, toward nonlinear optimization.
The measurement of productive efficiency is an issue of great interest. Since Farrell (Farrell, M.J., 1957. Journal of Royal Statistical Society, Series A 120, 253) implemented the first measure of technical efficienc...
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The measurement of productive efficiency is an issue of great interest. Since Farrell (Farrell, M.J., 1957. Journal of Royal Statistical Society, Series A 120, 253) implemented the first measure of technical efficiency, many researchers have developed new measures or have extended the already existing ones. The beginning of Data Envelopment Analysis (DEA) meant a new way of empirically measuring productive efficiency. Under some specific technologies, Farrell's measure was implemented giving rise to the first DEA models, CCR (Charnes, A., Cooper, W.W., Rhodes, E., 1978. European Journal of Operational Research 2, 429) and BCC (Banker, R.D., Charnes, A., Cooper, W.W.,1984. Management Science, 1078). The fact that these measures only account for radial inefficiency has motivated the development of the so-called Global Efficiency Measures (GEMs) (Cooper, W.W., Pastor, J.T., 1995. Working Paper, Departamento de Estadistica e Investigacion Operative, Universidad de Alicante, Alicante, Spain). In this paper we propose a new GEM inspired by the Russell Graph Measure of Technical Efficiency which avoids the computational and interpretative difficulties with this latter measure. Additionally, the new measure satisfies some other desirable properties. (C) 1999 Elsevier Science B.V. All rights reserved.
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