Optimal Channel Selection algorithm for CRahNs

As the data traffic is increasing, the spectrum bands are getting congested. It causes low latency and unreliable communication. Additional spectrum can be utilized to solve this problem but moving towards higher frequency means higher power requirement and increased cost. Cognitive radio network is another solution to this problem. It helps the nodes of a network to use the channels of the nearby bands which are not being used at that time. However, it has several challenges. One of these challenges is the transmission collision with the primary users of the network. Researchers have been working on this problem. However, it is still a major concern for the researchers. This paper proposes an algorithm that selects the optimal cognitive channel for the data transmission by the secondary user in such a way so that the transmission collision with the PU is minimized. After comparison with the existing latest similar protocol, the proposed protocol has shown 5.6% improvement in the throughput, 5.3% improvement in PDR. The delay is decreased by 0.6% and the transmission collision with PUs is reduced by 2.5%.     

偏好信息为模糊互反判断矩阵的模糊多属性决策法

研究只有部分权重信息且决策者对方案的偏好信息以模糊互反判断矩阵形式给出的模糊多属性决策问题。提出了一种基于目标规划模型的模糊多属性决策方法。该法首先基于模糊互反判断矩阵，利用转换函数将决策信息一致化，建立了一个目标规划模型．通过求解该模型确定属性的权重，然后运用加性加权法求出各方案的模糊综合属性值，并利用已有的三角模糊数排序公式求得决策方案的排序。文章最后把该法应用于解决风险投资领域中的项目评估问题。     

Strong duality for inexact linear programming

In this paper, we apply the Dubovitskii-Milyutin approach to derive strong duality theorems for inexact linear programming problems. Inexact linear programming deals with the standard linear problem in which the data is not well known and it is supposed to lie in certain given convex sets. The case of parametric dependence of the data is particularly analyzed and relations with semi-infinite and

semi-definite programming are also commented.     

A Semi-Infinite Programming Model In Data Envelopment Analysis

We consider a model for data envelopment analysis with infinitely many decision-making units. The determination of the relative efficiency of a given decision-making unit amounts to the solution of a semi-infinite optimization problem. We show that a decision-making unit of maximal relative efficiency exists and that it is 100% efficient. Moreover, this decision-making unit can be found by calculating a zero of the semi-infinite constraint function. For the latter task we propose a bi-level algorithm. We apply this algorithm to a problem from chemical engineering and present numerical results     

Constrained integer linear fractional programming problem

An integer linear fractional programming problem, whose integer solution is required to satisfy any h out of given n sets of constraints has been discussed in this paper. Method for ranking and scanning all integer points has also been developed and a numerical illustration is included in support of theory.     

Some generalizations of the criss-cross method for quadratic programming

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker’s, Cottle’s and Dantzig’s principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program

A finite criss-cross method, based on least-index resolution, is constructed for solving the LCP. In proving finiteness, orthogonality properties of pivot tableaus and positive semidefiniteness of quadratic matrices are used

In the last section some special cases and two further variants of the quadratic criss-cross method are discussed. If the matrix of the LCP has full rank, then a surprisingly simple algorithm follows, which coincides with Murty’s ‘Bard type schema’ in the P matrix case     

Column aggregation and primal decomposition in linear programming: some observations

In this paper we present a way to interpret column aggregation schemes in linear programming as a special kind of primal decomposition. This relation between aggregation and decomposition is obtained through a reformulation of the original problem by the introduction of auxiliary variables. The relation between aggregation and decomposition yields a natural iterative aggregation scheme, where weights updating can be done in different ways. We describe several weight updating schemes and illustrate three of them within an iterative aggregation technique with a numerical example. Finally we point out some new research issues that appear when the aggregation process is viewed in this decomposition framework     

Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ:-convex functions

Both parametric and nonparametric necessary and sufficient optimality conditions are established for a class of nonsmooth generalized fractional programming problems containing ρ-convex functions. Subsequently, these optimality criteria are utilized as a basis for constructing two parametric and four parameter-free duality models and proving appropriate duality theorems. Several classes of generalized fractional programming problems, including those with arbitrary norms, square roots of positive semidefinite quadratic forms, support functions, continuous max functions, and discrete max functions, which can be viewed as special cases of the main problem are briefly discussed. The optimality and duality results developed here also contain, as special cases, similar results for nonsmooth problems with fractional, discrete max, and conventional objective functions which are particular cases of the main problem considered in this paper     

Asymptotic analysis of a path-following barrier method for linearly constrained convex problems *

In the present paper the logarithmic barrier method applied to the linearly constrained convex optimization problems is studied from the view point of classical path-following algorithms. In particular, the radius of convergence of Newton's method which depends on the barrier parameter itself is estimated in standard norms, being independent of the parameter, without explicitly using self-concordance properties. The obtained results establish a parameter selection rule which guarantees the overall convergence of a barrier technique with only one Newton step at each parameter level and the complexity of the method can be estimated.