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.

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.

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.

The Optimal Conditions of the Linear Fractional Programming Problem with Constraint

在这篇文章，作者讨论线性部分编程问题的最佳的条件并且证明一个局部地可选的答案是一个全球性可选的答案，局部地最佳的答案能与限制状况在一个基本可行答案被达到。

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.

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

在这份报纸，一些必要、足够的 optimality 条件为包含 semilocal 电子 convex 和相关函数的部分多重客观编程被获得。另外，一些双结果在这种概括凸的功能下面被建立。我们的结果概括 Preda 获得的[J 数学肛门 Appl， 288 (2003 ) 365-382 ] 。

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 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 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.

下行RIS-NOMA的用户集群方法

为提高用户分布非均匀的场景下可重构智能表面(RIS)辅助下行非正交多址(NOMA)通信系统的性能,提出了一种分布式RIS辅助下行NOMA的用户聚类方案。首先,采用自适应几何分布(AGD)聚类算法划分用户集群(UCs),从而为各UC匹配RIS。然后,利用分式规划(FP)方法将非凸最大化频谱效率问题转换为凸优化问题。最后,为UC内用户逐级进行功率分配(PA)与被动波束形成(PB)。仿真结果表明,与谱聚类(SPC)、K均值(K-means)、高斯混合模型(GMM)聚类方案和正交多址(OMA)方案相比,在AGD方案下,功率对频谱效率提升了7%、14%、19%和42%的增益,反射面对频谱效率提升了16%、19%、26%和40%的增益。

面向大数据的数据库划分FP-Growth改进算法

提出了一种基于Hadoop架构和MapReduce编程模型实现的面向大数据的FP-Growth频繁项集挖掘的改进算法。首先将事务数据库按每个频繁1项进行抽取,生成对应的投影数据库,并将这些投影数据库分发到一个个节点机上;再由节点机对投影数据库进行划分,生成一个个规模更小的子数据库,并由节点机使用改进后的算法并行挖掘生成部分频繁项集;最后归并所有部分频繁项集得到全部的频繁项集。该算法无需像传统的FP-Growth算法一样为事务数据库生成庞大的FP树,有效解决了传统FP-Growth算法及其一些改进算法中因单机内存存储不下庞大的FP树而导致算法失效的问题。同时,由于所划分的子数据库规模接近,分发到各节点机上的负载更均衡,使得算法效率更高。

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.

STAR-RIS辅助通信感知一体化系统联合波束成形设计

提出同时将透射和反射可重构智能表面(Simultaneously transmitting and reflecting reconfigurable intelligent surfaces,STAR-RIS)与通信感知一体化(Integrated sensing and communication,ISAC)系统结合,以实现全空间的通信与感知。同时在STAR-RIS上应用一种低成本的传感器实现了在STAR-RIS上进行目标感知,解决了雷达感知的严重路径损耗问题。基于此,本文研究了STAR-RIS辅助位于STAR-RIS两侧的多用户多输入单输出(Multi-usermulti-input single-output,MU-MISO)以及一个位于STAR-RIS透射侧的目标的ISAC系统,旨在联合优化STAR-RIS的被动波束成形矩阵和ISAC基站处的主动波束成形矩阵,以最大化用户的通信和速率,同时满足目标感知的最低信噪比要求。为了解决优化过程中的非凸问题,提出了一种基于分式规划的块坐标上升算法,将优化变量分为几个块变量交替优化。在迭代优化后续波束成形问题上,应用了连续凸逼近和半正定松弛算法。与传统的可重构智能表面相比,仿真结果验证了在ISAC系统中部署STAR-RIS的优点。同时将所提的基于分式规划的算法与基于加权最小均方误差的算法进行了对比并验证了所提算法在提高通信和速率上的优势和有效性。

干扰场景下AIRS辅助的MISO系统资源分配算法

针对无线通信系统容易受到干扰而导致信息传输速率低的问题,提出了一种空中智能反射面(Aerial Intelligent Reflecting Surface,AIRS)辅助的多输入单输出(Multi-input Singleoutput,MISO)系统资源分配算法。首先,在考虑基站发射功率约束、AIRS相移约束和AIRS位置约束的条件下,建立了一个系统加权和速率最大化的资源分配问题。其次,利用拉格朗日对偶法转换原问题并将其分解为4个子问题,再应用分式规划、连续凸近似以及粒子群优化技术对子问题进行求解。最后,提出一种基于交替迭代的优化算法对原问题进行求解。仿真结果表明,所提方案与现有方案相比,能够实现更高的系统加权和速率,从而有效提升系统的抗干扰能力。