Topic
Concave function
About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.
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TL;DR: In this paper, an algorithm for minimizing a concave function over a convex polyedral set is given, which is based on the extension principle developed by Schoch and yields after a finite number of steps an exact optimal solution of the problem.
Abstract: For the problem of minimizing a concave function over a convex polyedral-set an algorithm is given, which is based on the extension principle developed by Schoch. This algorithm yields after a finite number of steps an exact optimal solution of the problem. On the other hand one can find out throughout the algorithm an approximate optimal solution with any given precision.
3 citations
01 Jan 1997
TL;DR: A common approach to many structured problems is partitioning in which the set of variables is split into two groups in such a way that the problem becomes remarkably easier when the values of the variables in the first group (which are called complicating variables) are temporarily fixed as mentioned in this paper.
Abstract: A common approach to many structured problems is partitioning in which the set of variables is split into two groups in such a way that the problem becomes remarkably easier when the values of the variables in the first group (which are called complicating variables) are temporarily fixed. Fundamental partitioning methods for mixed integer linear programming problems were developed in the 60’s (Benders (1962), Rosen (1964), Ritter (1967)) and ever since extended to nonlinear programming with many applications (Balas (1970), Geoffrion (1970), (1972)), Fleischmann (1973), Tind and Wolsey (1981), Burkard et al. (1985), Tuy (1987).
3 citations
TL;DR: In this article, a method of centers for solving multi-objective programming problems is proposed, where the objective functions involved are concave functions and the set of feasible points is convex.
3 citations
04 Dec 2009
TL;DR: The main focus of this paper is for decision analysis from the target-oriented point of view, and the target achievement computation method is revised, in which the resulting value function can have four shapes: concave, convex, S- shaped, inverse S-shaped.
Abstract: The main focus of this paper is for decision analysis from the target-oriented point of view. Firstly, the target achievement computation method is revised, in which the resulting value function can have four shapes: concave, convex, S-shaped, inverse S-shaped. In addition, it is now more and more widely acknowledged that all facets of uncertainty cannot be captured by a single probability distribution. A fuzzy uncertain target-oriented method is also proposed, in which the proportional approach is selected to transform a possibility distribution into its associated probability distribution, and then based on the random target-oriented model, we can obtain the probability of meeting targets. Three types of fuzzy targets, widely used in Bellman-Zadeh paradigm, are selected to illustrate the fuzzy target-oriented model.
3 citations
TL;DR: A modification of the column generation operation in Dantzig—Wolfe decomposition is suggested and it is shown how the subproblems may be solved parametrically in such a way as to maximize the immediate improvement in the value of objective in the “master problem”.
Abstract: A modification of the column generation operation in Dantzig--Wolfe decomposition is suggested. Instead of the usual procedure of solving one or more subproblems at each major iteration, it is shown how the subproblems may be solved parametrically in such a way as to maximize the immediate improvement in the value of objective in the "master problem", rather than to maximize the "reduced profit" of the entering column. The parametric problem is shown to involve the maximization of a piece-wise linear concave function of a single variable. It is hoped that in some cases the use of the suggested procedure may improve the slow rates of convergence common in decomposition algorithms.
3 citations