An inexact proximal point method for solving generalized fractional programs
In this paper, we present several new implementable methods for solving a generalized fractional program with convex data. They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these m...
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| Veröffentlicht in: | Journal of global optimization 2008-09, Vol.42 (1), p.121-138 |
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| creator | Strodiot, Jean-Jacques Crouzeix, Jean-Pierre Ferland, Jacques A. Nguyen, Van Hien |
| description | In this paper, we present several new implementable methods for solving a generalized fractional program with convex data. They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these methods, at each iteration a regularized parametric problem is solved inexactly to obtain an approximation of the optimal value of the problem. Since the parametric problem is nonsmooth and convex, we propose to solve it by using a classical bundle method where the parameter is updated after each ‘serious step’. We mainly study two kinds of such steps, and we prove the convergence and the rate of convergence of each of the corresponding methods. Finally, we present some numerical experience to illustrate the behavior of the proposed algorithms, and we discuss the practical efficiency of each one. |
| doi_str_mv | 10.1007/s10898-007-9270-x |
| format | Article |
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They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these methods, at each iteration a regularized parametric problem is solved inexactly to obtain an approximation of the optimal value of the problem. Since the parametric problem is nonsmooth and convex, we propose to solve it by using a classical bundle method where the parameter is updated after each ‘serious step’. We mainly study two kinds of such steps, and we prove the convergence and the rate of convergence of each of the corresponding methods. 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| subjects | Algorithms Approximation Computer Science Fractions Linear programming Mathematics Mathematics and Statistics Methods Operations Research/Decision Theory Optimization Real Functions Regularization methods Studies |
| title | An inexact proximal point method for solving generalized fractional programs |
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