An iterative approach to solve multiobjective linear fractional programming problems

This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to an efficient solution. A numerical example shows that this approach performs better than some existing algorithms. Randomly generated MOLFP problems are also solved to demonstrate the performance of new introduced algorithm.     

A globally convergent method for computing multiple vortices in a supersymmetric field theory

Computation of the solutions to the gauge field equations is known of great importance for the simulation of various particle physics systems. In this work, we establish a globally convergent iterative method for computing the multiple vortex solutions arising in a self-dual system of non-Abelian gauge field equations derived in a supersymmetric theory model. Using this method, we present a few numerical examples which demonstrate the effectiveness of the method and, at the same time, provide a concrete realization of the soliton-like behavior of the vortexlines concentrated around centers of vortices, which is believed to be essential for linear confinement in QCD.     

Symmetry and transformation properties of iterative ordinary differential equation

Symmetries of linear iterative equations and new conditions on the infinitesimals are obtained. Regarding the expressions of the solutions in terms of the parameters of the source equation, an ansatz is made on the original parameters. We have also obtained an expression for the source parameters of the transformed equation under equivalence transformations. We conducted this work with a special emphasis on second-, third- and fourth-order equations, although some of our results are valid for equations of a general order.     

Calculating particle pair potentials from fluid‐state pair correlations: Iterative ornstein–zernike inversion

An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this article. The new method, which is best referred to as Iterative Ornstein–Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique (Reith, Pütz and Müller‐Plathe, J. Comput. Chem. 2003, 24, 1624). Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant that is based on a trial bridge function in the Ornstein–Zernike integral equation formalism. As an input, the new method requires the particle pair correlations both in real space and in the Fourier conjugate wavenumber space. An accelerated iteration method is included in the discussion, by which the required number of iterations can be greatly reduced below that of the simple Picard iteration that underlies most common implementations of Iterative Boltzmann Inversion. Comprehensive tests with various pair potentials show that the new method generally surpasses the Iterative Boltzmann Inversion method in terms of reliability of the numerical solution for the particle pair potential. © 2018 Wiley Periodicals, Inc.     

Adaptive solution of infinite linear systems by Krylov subspace methods

In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, such as GMRES and QMR, embedded in the adaptive enlargement scheme, exhibit good performances.     

Vickrey–Dutch procurement auction for multiple items

We consider a setting where there is a manufacturer who wants to procure multiple items from a set of suppliers each of whom can supply one or more of these items (bundles). We design an ascending price auction for such a setting which implements the Vickrey–Clarke–Groves outcome and truthful bidding is an ex post Nash equilibrium. Our auction maintains non-linear and non-anonymous prices throughout the auction. This auction has a simple price adjustment step and is easy to implement in practice. As offshoots of this auction, we also suggest other simple auctions (in which truthful bidding is not an equilibrium by suppliers) which may be suitable where incentives to suppliers are not a big concern. Computer simulations of our auction show that it is scalable for the multi-unit case, and has better information revelation properties than its descending auction counterpart.     

一类抽象算子方程组的迭代解及其应用

在Banach空间中, 利用半序方法讨论了一类抽象算子方程组解的存在唯一性, 推广和统一了以前的一些结果. 然后应用到 Banach 空间非线性积分方程组, 得到了方程组的唯一解, 构造了收敛于方程组唯一解的迭代序列并给出了相应的误差估计.     

A two-echelon inventory model with lost sales

This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, R_i) control policy. The warehouse operates an (SQ, (S − 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for retailer i is the fixed transportation time L_i from the warehouse to that retailer. Otherwise retailer orders are met, after a delay, on a first-come first-served basis. The lead time on a warehouse order is fixed. Two further assumptions are made: that each retailer may only have one order outstanding at any time and that the transportation time from the warehouse to a retailer is not less than the warehouse lead time. The performance measures of interest are the average total stock in the system and the fraction of demand met in the retailers. Procedures for determining these performance measures and optimising the behaviour of the system are developed.     

A new family of iterative methods for solving system of nonlinear algebric equations

Homotopy perturbation method (HPM) is applied to construct a new iterative method for solving system of nonlinear algebric equations. Comparison of the result obtained by the present method with that obtained by revised Adomian decomposition method [Hossein Jafari, Varsha Daftardar-Gejji, Appl. Math. Comput. 175 (2006) 1–7] reveals that the accuracy and fast convergence of the new method.