This research article aims to study a multi-objective linear fractional programming (FMOLFP) problem having fuzzy random coefficients as well as fuzzy pseudorandom decision variables. Initially, the FMOLFP model is co...
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This research article aims to study a multi-objective linear fractional programming (FMOLFP) problem having fuzzy random coefficients as well as fuzzy pseudorandom decision variables. Initially, the FMOLFP model is converted to a single objective fuzzy linear programming (FLP) model. Secondly, we show that a fuzzy random optimal solution of an FLP problem is resolved into a class of random optimal solution of relative pseudorandom linear programming (LP) model. As a result, some of theorems show that a fuzzy random optimal solution of a fuzzy pseudorandom LP problem is combined with a series of random optimal solutions of relative pseudorandom LP problems. As an application, the developed approach is implemented to an inventory management problem by taking the parameters as trapezoidal fuzzy numbers, ultimately resulting in a new initiative for modelling real-world problems for optimization. In the last, some numerical examples are introduced to clarify the obtained results and their applicability.
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...
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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
The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower boun...
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The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower bound for the value of primal problem. Consequently, it is quite interesting to discuss the duality results for the case of second order. Thus, we focus our study on a discussion of duality relationships of a minimax fractional programming problem under the assumptions of second order B-(p, r)-invexity. Weak, strong and strict converse duality theorems are established in order to relate the primal and dual problems under the assumptions. An example of a non trivial function has been given to show the existence of second order B-(p, r)-invex functions.
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...
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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.
This article presents a fuzzy multi-objective linear fractional programming (FMOLFP) problem. The goal programming (GP) approach is used to solve the proposed problem. The LR (Left and Right) possibilistic variables a...
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This article presents a fuzzy multi-objective linear fractional programming (FMOLFP) problem. The goal programming (GP) approach is used to solve the proposed problem. The LR (Left and Right) possibilistic variables are addressed to the suggested the fuzzy multi-objective linear fractional programming (FMOLFP) model to deal the uncertainty of the model parameters. An auxiliary model in which objective function is the distance between the p- ary alpha- optimal value restriction and p-ary fuzzy objective function is proposed. In the last, one solved example is given to illustrate and to support the validity of the suggested approach.
We consider the problem of optimizing the ratio of two convex functions over a closed and convex set in the space of matrices. This problem appears in several applications and can be classified as a double-convex frac...
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We consider the problem of optimizing the ratio of two convex functions over a closed and convex set in the space of matrices. This problem appears in several applications and can be classified as a double-convex fractional programming problem. In general, the objective function is nonconvex but, nevertheless, the problem has some special features. Taking advantage of these features, a conditional gradient method is proposed and analyzed, which is suitable for matrix problems. The proposed scheme is applied to two different specific problems, including the well-known trace ratio optimization problem which arises in many engineering and data processing applications. Preliminary numerical experiments are presented to illustrate the properties of the proposed scheme.
In this paper, we present an outer approximation algorithm for solving, the following problem: max(x is an element ofS){f(x)/g(x)}, where f(x) greater than or equal to 0 and g(x) > 0 are d.c. (difference of convex)...
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In this paper, we present an outer approximation algorithm for solving, the following problem: max(x is an element ofS){f(x)/g(x)}, where f(x) greater than or equal to 0 and g(x) > 0 are d.c. (difference of convex) functions over a convex compact subset S of R-n. Let pi(lambda) = max(x is an element ofS)(f(x)-lambdag(x)), then the problem is equivalent to finding out a solution of the equation pi(lambda)=0. Though the monotonicity of pi(lambda) is well known, it is very time-consuming to solve the previous equation, because that maximizing (f(x)-lambdag(x)) is very hard due to that maximizing a convex function over a convex set is NP-hard. To avoid such tactics, we give a transformation under which both the objective and the feasible region turn to be d.c. After discussing some properties, we propose a global optimization approach to find an optimal solution for the encountered problem.
In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The concept of eta-bonvexity/generalized eta-bonvexity is adopted in order to discuss weak, stron...
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In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The concept of eta-bonvexity/generalized eta-bonvexity is adopted in order to discuss weak, strong and strict converse duality theorems.
The properties of linear fractional functions facilitate the usage of a well known scalar optimization problem that gives weakly efficient points. Separately, the weak efficiency can be detected with another scalar op...
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The properties of linear fractional functions facilitate the usage of a well known scalar optimization problem that gives weakly efficient points. Separately, the weak efficiency can be detected with another scalar optimization test based on the same properties. The numerical estimation of the nadir vector is considered as a possible application. (C) 2000 Elsevier Science B.V. All rights reserved.
In this paper a restricted class of multiobjective linear fractional programming problems in the sense that the denominators are identical is investigated. A numerical example is presented to illustrate the solution p...
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In this paper a restricted class of multiobjective linear fractional programming problems in the sense that the denominators are identical is investigated. A numerical example is presented to illustrate the solution procedure.
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