ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.

Sufficiency and Duality for Nondif ferentiable Multiobjective Fractional Programming Problems with (Φ,ρ,α)-V-Invexity

A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.

Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.

The Optimal Conditions of the Linear Fractional Programming Problem with Constraint

In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.

Optimality and Duality on Fractional Multi-objective Programming Under Semilocal E-convexity

In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288（2003） 365-382].

Solving the Interval-Valued Linear Fractional Programming Problem

This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.

DUALITY FOR MULTIOBJECTIVE FRACTIONAL PROGRAMMING INVOLVING n-SET FUNCTIONS

In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.

Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application

In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.

A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm

In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if βis negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.

A New Approach for Solving Linear Fractional Programming Problems with Duality Concept

Most of the current methods for solving linear fractional programming (LFP) problems depend on the simplex type method. In this paper, we present a new approach for solving linear fractional programming problem in which the objective function is a linear fractional function, while constraint functions are in the form of linear inequalities. This approach does not depend on the simplex type method. Here first we transform this LFP problem into linear programming (LP) problem and hence solve this problem algebraically using the concept of duality. Two simple examples to illustrate our algorithm are given. And also we compare this approach with other available methods for solving LFP problems.

The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified （C, α, p, d）-convexity

The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.

THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES

First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.

Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices

Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.

Duality Relations for a Class of a Multiobjective Fractional Programming Problem Involving Support Functions

In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

HIGHER-ORDER NON-SYMMETRIC DUALITY FOR NONDIFFERENTIABLE MINIMAX FRACTIONAL PROGRAMS WITH SQUARE ROOT TERMS

In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature.An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given.Various known results are discussed as particular cases.

Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi-Infinite Slab

Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.