Algorithm For Finding Approximate Solutions Research Articles

Iterative algorithms for a general system of generalized nonlinear mixed composite-type equilibria

In this paper, we consider and study a general system of generalized nonlinear mixed composite-type equilibria in Hilbert spaces. First, we prove the existence and uniqueness of the solution for this system of generalized nonlinear mixed composite-type equilibria. Second, the Mann iterative method with errors is extended to develop some new iterative algorithms for finding approximate solutions for this system of generalized nonlinear mixed composite-type equilibria. We also derive the strong convergence of the sequences generated by these iterative algorithms in Hilbert spaces.

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

1D numerical simulation of the mep mathematical model in ballistic diode problem

Numerical algorithms for finding approximate solutions of themacroscopic balance equations of charge transport in semiconductorsbased on the maximum entropy principle [A.M. Anile, V. Romano, Nonparabolic band transport in semiconductors: closure of the momentequations, Contin. Mech. Thermodyn. 11 (1999), 307--325; V.Romano, Non parabolic band transport in semiconductors: closure ofthe production terms in the moment equations, Contin. Mech.Thermodyn. 12(2000), 31--51] are constructed and discussedfor a typical 1D problem.

Strong Convergence of Iterative Algorithms for Variational Inequalities in Banach Spaces

Let C be a nonempty closed convex subset of a Banach space E with the dual E*, let T:C→E* be a Lipschitz continuous mapping and let S:C→C be a relatively nonexpansive mapping. In this paper, by employing the notion of generalized projection operator, we study the following variational inequality (for short, VI(T−f,C)): find x∈C such that $$\langle y-x,Tx-f\rangle\geq0,\quad\mbox{for all }y\in C,$$ where f∈E* is a given element. Utilizing the modified Ishikawa iteration and the modified Halpern iteration for relatively nonexpansive mappings, we propose two modified versions of J.L. Li’s (J. Math. Anal. Appl. 295:115–126, 2004) iterative algorithm for finding approximate solutions of VI(T−f,C). Moreover, it is proven that these iterative algorithms converge strongly to the same solution of VI(T−f,C), which is also a fixed point of S.

Symmetric low‐rank corrections to quadratic models

AbstractIn this paper, we study the quadratic model updating problems by using symmetric low‐rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low‐rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.

A NEW SYSTEM OF GENERALIZED CO-COMPLEMENTARITY PROBLEMS IN BANACH SPACES

In this paper, we introduce a new system of generalized cocomplementarity problems in Banach space. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are also obtained.

Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions

In the present paper, we introduce the concept of η -relaxed strong convexity of a differentiable functional and extend Ding and Yao’s auxiliary variational inequality technique [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Computers and Mathematics with Applications, 49 (2005), 857–869] to develop iterative algorithms for finding the approximate solutions to the mixed quasi-variational-like inclusion problem (in short, MQVLIP) in a Banach space. On the one hand, we establish a result on the existence of a solution to the equilibrium problem by virtue of well-known Brouwer’s fixed-point theorem. Moreover, by using this result we derive the existence and uniqueness of a solution to the MQVLIP and the existence of the approximate solutions generated by the algorithm for the MQVLIP. On the other hand, we use the concepts of η -relaxed strong convexity of a differentiable functional and η -cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the MQVLIP.

A NEW SYSTEM OF GENERALIZED CO-COMPLEMENTARITY PROBLEMS IN BANACH SPACES

In this paper, we introduce a new system of generalized cocomplementarity problems in Banach space. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are also obtained.

On the existence and convergence of approximate solutions for mixed variational-like inequalities

The auxiliary principle technique is extended to develop an iterative algorithm for finding approximate solutions of a mixed variational-like inequality in a real Hilbert space. Not only the existence of approximate solutions of a mixed variational-like inequality is proven, but also the strong convergence of approximate solutions to an exact solution of a mixed variational-like inequality is shown. The convergence criteria presented in this article are new.

Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities

The purpose of this paper is to investigate the iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities in a real Hilbert space, where the iterative algorithm is presented by virtue of the auxiliary principle technique. On one hand, the existence of approximate solutions of this class of mixed variational-like inequalities is proven. On the other hand, it is shown that the approximate solutions converge strongly to the exact solution of this class of mixed variational-like inequalities.

Multi-State Real-Time Bidirectional Search

This paper presents Multi-State Real-Time Bidirectional Search (MSRTBS), a method that improves the efficiency of the heuristic search algorithm for finding approximate solutions. Real-Time A* (RTA*) is a representative heuristic search algorithm for finding approximate solutions. The Multi-State Commitment (MSC) method was introduced into RTA* and dramatically improved the performance in problems such as the N-puzzle. As well, Real-Time Bidirectional Search (RTBS) also improved RTA* by changing a unidirectional search into a bidirectional one. This paper proposed a method that introduces MSC into RTBS. The experimental results showed that compared with RTBS and MSC our proposed method, MSRTBS, improved executed time and solution quality in the N-Puzzle.

Algorithm for generalized co-complementarity problems in Banach spaces

In this paper, we introduce a new class of generalized co-complementarity problems in Banach spaces. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are obtained.

On Generalized Mixed Quasivariational Inclusions

In this paper, we study a class of generalized mixed quasivariational in-clusions. By using the properties of the resolvent operator associated with maximal monotone mapping in real Hilbert space, we have established an existence theorem of solutions for generalized mixed quasivariational inclusions, suggesting a new iter-ative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solutions of the generalized mixed quasivariational inclusions. The results proved in this paper are more general than the previously known results in this area.

Gradient elements of the knapsack polytope

The knapsack problem is a classical NP-hard problem of special interest in combinatorial mathematics and complexity theory. Particularly interesting are the properties of the knapsack problem domain. In this paper we study the set of gradient elements of the knapsack polytope. They are related with the well-known greedy algorithm for finding approximate solutions to the optimization knapsack problem and constitute an important subset of the extremal elements (vertices) of the knapsack polytope. We obtain a tight bound for the number of distinct gradient elements, which is an exponential function of the problem dimension. We also use the greedy-algorithmic approach and the concept of gradient elements to devise a polynomial algorithm for a large subclass of a linear Diophantine problem which is a variant of the knapsack problem. Some optimization issues related to the problems considered are discussed as well.

Iterative algorithm for finding approximate solutions to completely generalized strongly quasivariational inequalities for fuzzy mappings

In this paper, we construct a new iterative algorithm, which includes many known algorithms as special cases to solve variational inequalities and quasivariational inequalities for fuzzy mappings. Further, we prove the convergence of the iterative sequences generated by this algorithm. Our results are the extension and improvements of the earlier and recent results in this field.

On a class of generalized nonlinear implicit quasivariational inclusions

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone mapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of, iterative sequence generated by the new algorithm is also given. As special cases, some known results in this field are also discussed.

Approximability of the Ground State Problem for Certain Ising Spin Glasses

We consider polynomial time algorithms for finding approximate solutions to the ground state problem for the following three-dimensional case of an Ising spin glass: 2nspins are arranged on a two-level grid with at mostnγvertical interactions (0 ≤ γ ≤ 1). The main results are:1.Let12≤ γ < 1. There is an approximate polynomial time algorithm with absolute error less thannγfor alln; there exists a constant β > 0 such that every approximate polynomial time algorithm has absolute error greater than βnγinfinitely often, unlessP=NP.2.Let γ = 1. There is an approximate polynomial time algorithm with absolute error less thann/lgn; there exists a numberk> 1 such that every approximate polynomial time algorithm has absolute error greater thann/(lgn)kinfinitely often iffNP⊈ ∩ε > 0DTIME(2nε).

Perturbed Proximal Point Algorithms for Generalized Quasivariational Inclusions

In this paper, we study a class of generalized quasivariational inclusions. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert space, we have established an existence theorem of solutions for generalized quasivariational inclusions, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions. As special cases, some known results in this field are also discussed.

Site Partitioning for Redundant Arrays of Distributed Disks

Redundant arrays of distributed disks (RADD) can be used in a distributed computing system or database system to provide recovery in the presence of disk crashes and temporary and permanent failures of single sites. In this paper, we look at the problem of partitioning the sites of a distributed storage system into redundant arrays in such a way that the communication costs for maintaining the parity information are minimized. We show that the partitioning problem is NP-hard. We then propose and evaluate several heuristic algorithms for finding approximate solutions. Simulation results show that significant reduction in remote parity update costs can be achieved by optimizing the site partitioning scheme.

Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities

In this paper, we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include. as a special case, some known results in this field. Our results are the extension and improvements of the results of Siddiqi and Ansari, Ding, and Zeng.