In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a 2-approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated facility location algorithm achieves the inte...

As a kind of particular programming, transportation problem draws much attention in many fields such as energy development, materials management, etc. In this paper, by analyzing the essence of stochastic programming and the deficiencies of existing methods, we propose a comparison method based on synthesizing effect for the standard to judge an objective value is good or not, and give the axio...

abstract it is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (cc) problem. for this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. a samp...

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newt...

Quasi-Newton methods based on least change secant updating formulas that solve linear equations Ax = b in n = dim(x) = dim(b) steps can be expected to solve corresponding smooth nonlinear systems n-step quadratically, i.e. with an r-order of ρ = 2 = 1 + 1/n+O(1/n). The best rate one can possibly expect on general problems is given by the positive root ρn of ρ (ρ− 1) = 1, for which ρn − 1 = ln(n...

using the mathematic techniques such as fuzzy approach has useful outcomes for production planning in different sources. in this paper lgp1 was used to model the objectives such as: avoidance of shortage or surplus of demand, access to maximum of income, using the normal capacity of production and organizing the inventory of warehouse, within the framework of goal constraints like balancing be...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

This paper presents a new Discriminative Random Fields (DRFs) framework. Based on the DRFs framework proposed by Kumar and Hebert, the following improvements have been conducted. Firstly, the interaction potential and the associated potential model are simplified. Secondly, we reduce the dimension of the multi-scale features, re-definedimension of the single-scale feature, and increase the colo...