A moving mesh method in multiblock domains with application to a combustion problem

A moving mesh method for structured grids is presented for general solution domains, which are composed of a number of simply shaped blocks. Its basic idea is to solve moving mesh PDEs by overlapping Schwarz iterations and to connect the meshes in each of the blocks smoothly. A finite element method based upon this moving mesh method is developed for solving time dependent PDEs and validated for the problem of laminar flame propagation in an obstacled channel. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 449–467, 1999     

Bounds for the quadratic assignment problem using the bundle method

Semidefinite programming (SDP) has recently turned out to be a very powerful tool for approximating some NP-hard problems. The nature of the quadratic assignment problem (QAP) suggests SDP as a way to derive tractable relaxations. We recall some SDP relaxations of QAP and solve them approximately using a dynamic version of the bundle method. The computational results demonstrate the efficiency of the approach. Our bounds are currently among the strongest ones available for QAP. We investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree.      

A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization

In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α$\alpha$-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)].     

On the complexity of a bundle pricing problem

We consider the problem of pricing items in order to maximize the revenue obtainable from a set of single minded customers. We relate the tractability of the problem to structural properties of customers’ valuations: the problem admits an efficient approximation algorithm, parameterized along the inhomogeneity of the valuations.     

Spectral Galerkin method and its application to a Cauchy problem of Helmholtz equation

Based on a mathematical model of laser beams, we present a spectral Galerkin method for solving a Cauchy problem of the Helmholtz equation in a rectangle, where the Cauchy data pairs are given at y?=?0 and boundary data are for x?=?0 and x?=?π. The solution is sought in the interval 0?<?y?<?1. The spectral Galerkin method is considered as a regularization method. We then perform an analysis on the error bound for this method. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method.     

On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem

In this paper, we couple regularization techniques of nondifferentiable optimization with the h‐version of the boundary element method (h‐BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example, we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by an h‐BEM. We prove convergence of the h‐BEM Galerkin solution of the regularized problem in the energy norm, provide an a priori error estimate and give a numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

A spectral bundle method with bounds

Semidefinite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primal-dual interior point methods can take much time even for problems of moderate size. The recent spectral bundle method of Helmberg and Rendl can solve quite efficiently large structured equality-constrained semidefinite programs if the trace of the primal matrix variable is fixed, as happens in many applications. We extend the method so that it can handle inequality constraints without seriously increasing computation time. In addition, we introduce inexact null steps. This abolishes the need of computing exact eigenvectors for subgradients, which brings along significant advantages in theory and in practice. Encouraging preliminary computational results are reported. Received: February 1, 2000 / Accepted: September 26, 2001?Published online August 27, 2002 RID="*" ID="*"A preliminary version of this paper appeared in the proceedings of IPCO ’98 [12].     

An incremental bundle method for portfolio selection problem under second-order stochastic dominance

Numerical Algorithms - We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize...     

An application of the monotone iterative method to a combustion problem in porous media

Problems related to combustion fronts in porous media have been studied by many authors recently, see e.g. [Y. Akkutlu, Y.C. Yortsos, The dynamics of in-situ combustion fronts in porous media, Combust. Flame 134 (2003) 239–247; J.C. da Mota, W. Dantas, D. Marchesin, Combustion fronts in porous media, SIAM J. Appl. Math. 62 (2002) 2175–2198; D.A. Schult, B.J. Matkowsky, V.A. Volpert, A.C. Fernandez-Pello, Forced forward smolder combustion, Combust. Flame 104 (1996) 1–26]. Most of this interest is due to the combustion process for oil recovery.In this paper we construct monotone iteractions for a Cauchy problem arising from a combustion model in a porous medium derived in [J.C. da Mota, S. Schecter, Combustion fronts in a porous medium with two layers, J. Dynam. Differential Equations 18 (3) (2006) 615–665]. We conclude that the monotone iteractions converge to a unique solution of this Cauchy problem, globally in time.     

Some unilateral Korn inequalities with application to a contact problem with inclusions

In the first part of this note, some unilateral inequalities of the Korn type are established. These inequalities seem to be new.In the second part, these inequalities are used in an essential way to prove the existence of a solution (which is not necessarily unique) for a unilateral contact problem involving a matrix material with inclusions of various shapes (the conditions depend on the shape of each inclusion in a remarkable way).     

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

This paper is devoted to the study of a resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high availability real-time distributed systems. Informally, this problem consists, starting from an arbitrary initial distribution of processes on the processors of a distributed system, in finding the least disruptive sequence of operations (non-impacting process migrations or temporary process interruptions) at the end of which the system ends up in another predefined arbitrary state. The main constraint is that the capacity of the processors must not be exceeded during the reconfiguration. After a brief survey of the literature, we prove the NP-hardness of the problem and exhibit a few polynomial special cases. We then present a branch-and-bound algorithm for the general case along with computational results demonstrating its practical relevance. The paper is concluded by a discussion on further research.     

同伦方法求解非凸区域Brouwer不动点问题

本文构造了一个新的求解非凸区域上不动点问题的内点同伦算法,并在弱法锥(见定义2．1(2))和适当的条件下,证明了算法的全局收敛性．本文所给的条件比外法锥条件更加一般．     

Nonconvex variational problem with recursive integral functionals in Sobolev spaces: Existence and representation

The purpose of this paper is twofold. First, we present the existence theorem of an optimal trajectory in a nonconvex variational problem with recursive integral functionals by employing the norm-topology of a weighted Sobolev space. We show the continuity of the integral functional and the compactness of the set of admissible trajectories. Second, we show that a recursive integrand is represented by a normal integrand under the conditions guaranteeing the existence of optimal trajectories. We also demonstrate that if the recursive integrand satisfies the convexity conditions, then the normal integrand is a convex function. These results are achieved by the application of the representation theorem in Lp-spaces.     

A control problem with application to integral inequalities

The paper deals with extensions of Carlitz and Cohen et al. of the Brock recurrence relation, which occurs in a sorting problem, and is connected with generating functions of the Jacobi polynomial. New expressions are also presented regarding the positivity of coefficients in the power series expansions of rational functions.