This bibliography of fractional programming is a continuation of five previous bibliographies by the author (Pure Appl. Math. Sci. (India), Vol. XIII, No. 1-2, 35-69, March (198 1);ibid. Vol. XVII, No. 1-2, 87-102, Ma...
详细信息
This bibliography of fractional programming is a continuation of five previous bibliographies by the author (Pure Appl. Math. Sci. (India), Vol. XIII, No. 1-2, 35-69, March (198 1);ibid. Vol. XVII, No. 1-2, 87-102, March (1983);ibid. XXII, No. 1-2, 109-122, September (1985);Optimization 23(1992)1, 53-71;ibid. 45(1999) 1-4, 343-367). This compilation lists, in alphabetical order by the name of the first author, 491 papers dealing with fractional programming and its applications. This covers mainly the period 19972005 but it also includes some references published up to 1997 which were not included in the previous bibliographies or which were mentioned as 'to appear' in the five bibliography. In compiling this list we used Mathematical Reviews, Zentralblatt fur Mathematik, Referativnyi Zhurnal (Matematika) and Current Papers on Computers & Control. The papers are either published in some form (in technical journals or as internal reports) or are available only as typewritten manuscripts (for example, as doctoral theses or as papers presented at scientific sessions). If a work was first published as an internal report, and later in a technical journal, both publications are cited, since it may occasionally be easier for anyone seeking literature to find a copy of the internal report. The organization of the bibliography is the same as that used previously i.e., the references are classified into one or more of 15 sections by their basic contents and there is an author index in alphabetical order. In an undertaking of this scope and nature some errors are inevitable, despite elaborate precautions and checks. The author will be grateful for any corrections, additions or comments about this bibliography.
A higher-order dual for a non-differentiable minimax fractional programming problem is formulated. Using the generalized higher-order eta-convexity assumptions on the functions involved, weak, strong and strict conver...
详细信息
A higher-order dual for a non-differentiable minimax fractional programming problem is formulated. Using the generalized higher-order eta-convexity assumptions on the functions involved, weak, strong and strict converse duality theorems are established in order to relate the primal and dual problems. Results obtained in this paper naturally unify and extend some previously known results on non-differentiable minimax fractional programming in the literature. MSC: 26A51;90C32;49N15
In this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This metho...
详细信息
In this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This method is based on the conjugate gradient projection method, so that we start with a feasible point and then a sequence of feasible directions towards all efficient adjacent extremes of the problem can be generated. Since methods based on vertex information may encounter difficulties as the problem size increases, we expect that this method will be less sensitive to problem size. A simple production example is given to illustrate this method.
Multiple objective linear fractional programming (MOLFP) is an important field of research. Using some branch and bound techniques, we have developed a new interactive method for MOLFP that drastically reduces the com...
详细信息
Multiple objective linear fractional programming (MOLFP) is an important field of research. Using some branch and bound techniques, we have developed a new interactive method for MOLFP that drastically reduces the computational effort needed, while providing guidance for the decision maker in the choice of his/her preferred solutions. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions while constraining the others. Several linear programming problems, organized in a tree structure, are generated as the search evolves. The whole idea is simple and it results in a fast and very intuitive approach to exploring the non-dominated set of solutions in MOLFP, and eventually to finding the preferred solution.
In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a...
详细信息
In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-Lojasiewicz property.
We propose a solution strategy for fractional programming problems of the form max x∈x g(x)/ φ(u(x)), where the functionφ satisfies certain convexity conditions. It is shown that subject to these conditions optima...
详细信息
We propose a solution strategy for fractional programming problems of the form max x∈x g(x)/ φ(u(x)), where the functionφ satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max x∈x g(x) + λu(x), whereλ is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.
This paper integrates fuzzy linearization strategy, goal programming, a membership function and conditional control mechanisms to produce a novel method to deal with the binary behavior of multiple objective fractiona...
详细信息
This paper integrates fuzzy linearization strategy, goal programming, a membership function and conditional control mechanisms to produce a novel method to deal with the binary behavior of multiple objective fractional programming problems and multiple objective fractional programming problems with a utility function. The major contributions of the proposed method are twofold. (1) The binary behavior of multiple objective fractional programming problems can easily be converted into a linearized program using the proposed fuzzy linearization strategy. The linearized program can easily be solved, using commercial linear programming packages, yielding an approximate global optimal solution, and (2) The utility function is also used to ensure that the qualification requirements for a multiple objective fractional programming problem are met, in contrast to most past mathematical approaches, which only use quantitative approaches to deal with such a problem. In addition, an illustrative example and a practical real case are provided to demonstrate the usefulness of the proposed model. The discussion of the practical problem will help decision makers to realize the usefulness of a utility function and the binary behavior in multiple objective fractional programming problems. (C) 2017 Elsevier Ltd. All rights reserved.
The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn't possess any convexity propriet...
详细信息
The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn't possess any convexity propriety. In this paper, we propose a method that generates the set of the efficient solutions of multiobjective integer linear plus linear fractional programming problem. Our method consists in Branch-and-Bound exploration combined with cutting plane technique that allows to remove from search inefficient solutions. The cutting plane technique takes into account the inefficiency of a solution in another problem that implies the inefficiency of that solution in our problem and uses this link to reduce the exploration's domain.
We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n-set functions.
We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n-set functions.
暂无评论