共查询到20条相似文献,搜索用时 609 毫秒
1.
《Optimization》2012,61(5):675-682
We consider the problem how a convex optimal-value function arising in primal decomposition can be finitely continued beyond its domain. By a suitable presentation of the exact penalty method an implementable continuation can be obtained which does not change the set of optimal solutions. If the problem has separability and partially linearity properties we manage to obtain a complete continuation of the optimal-value function. 相似文献
2.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):243-268
In this paper, we are interested in the solution of a viscous scalar conservation law. We remark that its first order spatial derivatives solve a system of partial differential equations presenting a nonlocal nonlinearity. We associate a nonlinear martingale problem with this system. After proving existence and uniqueness for the martingale problem, we obtain a propagation of chaos result for a system of interacting diffusion processes. We deduce that it is possible to approximate the solution of the viscous scalar conservation law thanks to the interacting diffusions 相似文献
3.
4.
Summary. This paper describes the numerical analysis of a time dependent linearised fluid structure interaction problems involving
a very viscous fluid and an elastic shell in small displacements. For simplicity, all changes of geometry are neglected. A
single variational formulation is proposed for the whole problem and generic discretisation strategies are introduced independently
on the fluid and on the structure. More precisely, the space approximation of the fluid problem is realized by standard mixed
finite elements, the shell is approximated by DKT finite elements, and time derivatives are approximated either by midpoint
rules or by backward difference formula.
Using fundamental energy estimates on the continuous problem written in a proper functional space, on its discrete equivalent,
and on an associated error evolution equation, we can prove that the proposed variational problem is well posed, and that
its approximation in space and time converges with optimal order to the continuous solution.
Received May 14, 1999 / Revised version revised October 14, 1999 / Published online July 12, 2000 相似文献
5.
Alfred K. Louis 《Numerische Mathematik》1986,48(3):251-262
Summary The reconstruction of an object from its x-ray scans is achieved by the inverse Radon transform of the measured data. For fast algorithms and stable inversion the directions of the x rays have to be equally distributed. In the present paper we study the intrinsic problems arising when the directions are restricted to a limited range by computing the singular value decomposition of the Radon transform for the limited angle problem. Stability considerations show that parts of the spectrum cannot be reconstructed and the irrecoverable functions are characterized. 相似文献
6.
Summary Variational principles are important tools for the approximate solution of boundary-value problems. There are many types of variational principles, and each has its advantages and disadvantages. In this paper we show how to use a combination of variational principles, each for a given subregion of the underlying region of space, so as to best utilize the chief benefits of the individual principles. Such a patched principle is particularly useful in solving transonic flow problems, where we use different principles in the elliptic and hyperbolic regions. We present the results of some numerical experiments for the Tricomi problem. These seem to indicate that our patched principle, when used in conjunction with the finite element method, leads to accuracy which is second-order in the mesh spacing, as compared to the standard numerical methods of solving this problem, which are only first-order. 相似文献
7.
Herbert Arndt 《Numerische Mathematik》1984,43(3):343-360
Summary Retarded initial value problems are routinely replaced by an initial value problem of ordinary differential equations along with an appropriate interpolation scheme. Hence one can control the global error of the modified problem but not directly the actual global error of the original problem. In this paper we give an estimate for the actual global error in terms of controllable quantities. Further we show that the notion of local error as inherited from the theory of ordinary differential equations must be generalized for retarded problems. Along with the new definition we are led to developing a reliable basis for a step selection scheme. 相似文献
8.
《Optimization》2012,61(4):523-535
In this paper we study the relation between the general concept for an optimal solution for stochastic programming problems with a random objective function-the concept of an £-efficient solution-and the associated parametric problem, We show that it is possible under certain assumptions to obtain some or even all £-efficient solutions of the stochastic problem by solving the parametric problem with respect to a certain parameter set. 相似文献
9.
10.
András Frank 《Mathematical Programming》1999,84(3):565-576
In order to unify these approaches, here we describe a two-phase greedy algorithm working on a slight extension of lattice
polyhedra. This framework includes the rooted node-connectivity augmentation problem, as well, and hence the resulting algorithm,
when appropriately specialized, finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity
by one. The only known algorithm for this problem used submodular flows. Actually, the specialized algorithm solves an extension
of the rooted edge-connectivity and node-connectivity augmentation problem.
Received December 1996 / Revised version received January 1998
Published online March 16, 1999 相似文献
11.
Arian Novruzi 《Numerische Mathematik》2001,88(1):185-201
Summary. In this paper we establish a error estimation on the boundary for the solution of an exterior Neumann problem in . To solve this problem we consider an integral representation which depends from the solution of a boundary integral equation.
We use a full piecewise linear discretisation which on one hand leads to a simple numerical algorithm but on the other hand
the error analysis becomes more difficult due to the singularity of the integral kernel. We construct a particular approximation
for the solution of the boundary integral equation, for the solution of the Neumann problem and its gradient on the boundary
and estimate their error.
Received May 11, 1998 / Revised version received July 7, 1999 / Published online August 24, 2000 相似文献
12.
《Optimization》2012,61(2):203-221
We propose an (α,β)-optimal solution concept of fuzzy optimization problem based on the possibility and necessity measures. It is well known that the set of all fuzzy numbers can be embedded into a Banach space isometrically and isomorphically. Inspired by this embedding theorem, we can transform the fuzzy optimization problem into a biobjective programming problem by applying the embedding function to the original fuzzy optimization problem. Then the (α,β)-optimal solutions of fuzzy optimization problem can be obtained by solving its corresponding biobjective programming problem. We also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed as fuzzy numbers). Under a setting of core value of fuzzy numbers, we provide the Karush–Kuhn–Tucker optimality conditions and show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also a (1,1)-optimal solution of the original fuzzy optimization problem. 相似文献
13.
Peter Knabner 《Numerische Mathematik》1985,46(3):429-442
Summary We investigate the following problem: To influence a heat conduction process in such a way that the conductor melts in a prescribed manner. Since we treat a linear auxiliary problem, it suffices to deal with a linear-quadratic defect minimization problem with linear restrictions, where we use splines or polynomials as approximation spaces. In case of exact controllability we derive various order of convergence estimates, which we discuss for some numerical examples. 相似文献
14.
Alastair Spence 《Numerische Mathematik》1978,29(2):133-147
Summary Approximate solutions of the linear integral equation eigenvalue problem can be obtained by the replacement of the integral by a numerical quadrature formula and then collocation to obtain a linear algebraic eigenvalue problem. This method is often called the Nyström method and its convergence was discussed in [7]. In this paper computable error bounds and dominant error terms are derived for the approximation of simple eigenvalues of nonsymmetric kernels. 相似文献
15.
Chuanming Zong 《Monatshefte für Mathematik》2005,145(1):73-81
In this article we study the following problem: Is the covering (packing) density of a Cartesian product of two convex bodies always equal to the product of their corresponding covering (packing) densities? For the covering case we get a negative answer. For the packing case we get a combinatorial version which seems to be important for its own interest. 相似文献
16.
《Optimization》2012,61(4-5):507-528
In this article, we study semi-definite and semi-infinite programming problems (SDSIP), which includes semi-infinite linear programs and semi-definite programs as special cases. We establish that a uniform duality between the homogeneous (SDSIP) and its Lagrangian-type dual problem is equivalent to the closedness condition of certain cone. Moreover, this closedness condition was assured by a generalized canonically closedness condition and a Slater condition. Corresponding results for the nonhomogeneous (SDSIP) problem were obtained by transforming it into an equivalent homogeneous (SDSIP) problem. 相似文献
17.
Summary.
The aim of this work is to study a decoupled algorithm of
a fixed point for solving a
finite element (FE) problem for the approximation of viscoelastic
fluid flow obeying an Oldroyd B differential model. The interest for
this algorithm lies in its applications to numerical simulation and
in the cost of computing. Furthermore it is easy to bring this
algorithm into play.
The unknowns
are
the viscoelastic part of the extra stress tensor,
the velocity and
the pressure.
We suppose that the solution
is sufficiently
smooth and small. The approximation
of stress, velocity and pressure are resp.
discontinuous,
continuous,
continuous FE. Upwinding needed for convection of
, is made
by discontinuous FE. The method consists to
solve alternatively a transport equation for the stress,
and a Stokes like problem for velocity and pressure. Previously,
results of existence of the solution for the approximate problem and
error bounds have been obtained using fixed point
techniques with coupled algorithm.
In this paper we show that the mapping of the decoupled
fixed point algorithm is locally (in a neighbourhood of
)
contracting and we obtain existence, unicity (locally) of the solution
of the approximate problem and error bounds.
Received
July 29, 1994 / Revised version received March 13, 1995 相似文献
18.
Jianliang Li Hua Zhu Xianzhong Zhou Wenjing Song 《高等学校计算数学学报(英文版)》2006,15(4):299-305
The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm. 相似文献
19.
Summary.
The design of cost-efficient networks satisfying certain
survivability constraints
is of major concern to the telecommunications industry.
In this paper we study a problem of extending
the capacity of a network by discrete steps as cheaply as possible,
such that the given traffic demand can be accommodated
even when a single edge or node in the network fails.
We derive valid and nonredundant inequalities
for the polyhedron of capacity design variables,
by exploiting its relationship to connectivity network design
and knapsack-like subproblems.
A cutting plane algorithm and heuristics for the problem
are described,
and preliminary computational results are reported.
Received August 26, 1993 / Revised version received
February 1994 相似文献
20.
Convergence of Newton's method for convex best interpolation 总被引:7,自引:0,他引:7
Summary. In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type
method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of
a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. [17] and settle the question of
its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency
of the proposed global strategy is confirmed with numerical experiments.
Received October 26, 1998 / Revised version received October 20, 1999 / Published online August 2, 2000 相似文献