Global linear convergence of a path-following algorithm for some monotone variational inequality problems

We consider a primal-scaling path-following algorithm for solving a certain class of monotone variational inequality problems. Included in this class are the convex separable programs considered by Monteiro and Adler and the monotone linear complementarity problem. This algorithm can start from any interior solution and attain a global linear rate of convergence with a convergence ratio of 1 ?c/√m, wherem denotes the dimension of the problem andc is a certain constant. One can also introduce a line search strategy to accelerate the convergence of this algorithm.     

Gauss-seidel method for least-distance problems

In this paper, we reformulate the least-distance problems with bounded inequality constraints as an unconstrained convex minimization problem, which is equivalent to a system of piecewise linear equationsA(a+A ^T y) _c ^d =b. The proposed Gauss-Seidel method for solving the problems is easy to implement and behaves very well when the number of rows ofA is much less than the number of columns ofA. Moreover, we prove that the Gauss-Seidel method has a linear convergence rate.The authors would like to thank Jinshui Qin who did some preliminary numerical testing for their research.     

Exploiting additional structure in equality constrained optimization by structured SQP secant algorithms

In 1988, Tapia (Ref. 1) developed and analyzed SQP secant methods in equality constrained optimization taking explicitly the additive structure of the problem setting into account. In this paper, we extend Tapia's augmented scale Lagrangian secant method to the case where additional structure coming from the objective function is available. Using the example of nonlinear least squares with equality constraints, we demonstrate these ideas and develop a convergence theory proving local and q-superlinear convergence for this kind of structured SQP-algorithms.This research was supported by the Studienstiftung des Deutschen Volkes.     

Accuracy of a deterministic particle method for Navier-Stokes equations

The accuracy of a deterministic particle method in approximating the solution of the Navier-Stokes equations is investigated. The convective part is solved using a classical vortex method for inviscid fluids, and an iterative procedure is added to improve the interpolation of the vorticity function. In our examples the vorticity is radially symmetric. For a regular initial data, a discrete quadratic error on the velocity and the vorticity is considered. Otherwise, for a singular initial data, the exact and computed angular moments of the vorticity are compared.     

A difference scheme for a parabolic system modelling the thermoelastic contacts of two rods

In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that each rod is fixed at one end and is free to expand or contact at the other end. A finite difference scheme is derived by the method of reduction of order on nonuniform mesh. The unique solvability, unconditional stability, and convergence of the difference scheme are proved. The convergence order is of order two in both time and space. The convergence of iterative algorithm for the difference scheme are also discussed. A numerical example is presented to demonstrate the theoretical results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

ＣＯＮＶＥＲＧＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳ　ＦＯＲＲＬＣ－ＮＯＮＬＩＮＥＡＲＮＥＴＷＯＲＫＳＷＩＴＨＴＩＭＥ－ＶＡＲＹＩＮＧＥＬＥＭＥＮＴＳ￥ＪｉａｎｇＪｉｊａ（蒋断发）（Ｄａｐｔ．ｏｆＭａｔｈ．，ＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃ...     

An infeasible-interior-point predictor-corrector algorithm for theP *-geometric LCP

AP _*-geometric linear complementarity problem (P _*GP) as a generalization of the monotone geometric linear complementarity problem is introduced. In particular, it contains the monotone standard linear complementarity problem and the horizontal linear complementarity problem. Linear and quadratic programming problems can be expressed in a “natural” way (i.e., without any change of variables) asP _*GP. It is shown that the algorithm of Mizunoet al. [6] can be extended to solve theP _*GP. The extended algorithm is globally convergent and its computational complexity depends on the quality of the starting points. The algorithm is quadratically convergent for problems having a strictly complementary solution. The work of F. A. Potra was supported in part by NSF Grant DMS 9305760     

Hermite—Fejér Interpolation for Rational Systems

This paper considers Hermite—Fejér and Grünwald interpolation based on the zeros of the Chebyshev polynomials for the real rational system P _n (a ₁ , . . . , a _n ) with the nonreal poles in {a}ⁿ _k=1 C\[-1,1] paired by complex conjugation. This extends some well-known results of Fejér and Grünwald for the classical polynomial case. July 11, 1996. Dates revised: January 6, 1997 and July 30, 1997.     

Maluta's coefficient in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

Maluta's coefficient of Musielak-Orlicz sequence spaces equipped with the Orlicz norm is calculated. A sufficient condition for the Schur property of these spaces is given.

     

THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 < p < 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.