a. fakharzadeh

Recently, absolute value equations (AVEs) are lied in theconsideration center of some researchers since they are very suitable al-ternatives for many frequently occurring optimization problems. There-fore, nding a fast solution method for these type of problems is verysignicant. In this paper, based on the mixed-type splitting (MTS) ideafor solving linear system of equations, a new fast algorithm for solvingAVEs is presented. This algorithm has two auxiliary matrices whichare limited to be nonnegative strictly lower triangular and nonnega-tive diagonal matrices. The convergence of the algorithm is discussedvia some theorems. In addition, it is shown that by suitable choice ofthe auxiliary matrices, the convergence rate of this algorithm is fasterthan that of the SOR, AOR, Generalized Newton, Picard and SOR-like methods. Eventually, some numerical results for dierent size ofproblem dimensionality are presented which admit the credibility of theproposed algorithm.

Data envelopment analysis (DEA) is a nonparametric method aimed to estimate production frontiers. This technique has been empirically used to measure the productive efficiency of decision making units (  comprising a wide range of entities (i.e. banks, car makers, schools) in terms of their inputs conversion into outputs. The decision makers are challenged with the problem of restricted resources and optimal allocation of budget to each DMU. The common budget allocating models (except those having series internal processes) do not seriously address the internal processes of the DMUs. That is, they are overlooked and rather passed up as block boxes. This paper proposed a new model for optimal budgeting for designing dynamic network system using DEA implication. The advantages of this model (which can be regarded as the first accomplishment) are expounded through the research body. Within the framework of the dynamic network systems of optimal system design (OSD) via insights gained by DEA, the optimal budgeting, the budget deficit and the budget congestion along with superior features of the proposed model were systematically investigated. Finally, two cases were presented on which the suggested model was applied. In one application, the OSD network of a business entity with 5 DMUs was addressed; while the other one dealt with a business venture with 24 DMUs.

In this paper, a revised measure-theoretical approach is applied for solving some classical optimal control problems. Indeed, the problem is converted into an optimization problem in measure space and then it is transformed into a finite dimensional nonlinear programming problem by using approximation scheme. At last, the nearly optimal control and trajectory functions are determined from the solution of the nonlinear optimization problem. A numerical example is given to demonstrate the efficiency of this method.

By a brief review on the applications of wavelets in solving optimal control problems, a multiresolution analysis for two dimensional Sobolev spaces and the square spline wavelets are considered. Regarding the density and approximation properties of these wavelets, for the first time, they are employed for solving optimal control problems by embedding method. Existence and the determination way for the solution are also discussed. Finally, the abilities of the new approach are explained by a numerical example and some comparisons.