摘要:

We consider an approach to determine parameters in a system of one-dimensional time-dependent parabolic differential equations and coupled ordinary differential equations. The model allows transmission conditions between separate integration areas for functions and derivatives. Proceeding from given experimental data, e.g. observation times and measurements, the minimum least squares distance of the measured data from the solution of the dynamical system at designated space values is to be computed. The method of lines is used to discretize the partial differential equation with respect to polynomials of arbitrary odd order, and to transform the original system into a sequence of ordinary differential equations, that can be solved then by any available ODE-solver. Numerical test results are included to show the efficiency of different ODE solvers and optimization routines based on a collection of 20 test models

ISSN:1055-6788    

DOI:10.1080/10556789708805655

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The application of a multilevel Newton method for the numerical solution of an optimal control problem governed by a phase field model is investigated. The phase field model is used to describe the phase change (e.g. liquid to solid) of materials and is given as a system of two semilinear parabolic equations. For the solution of the optimal control problem the necessary optimality conditions are reformulated as a compact fixed point problem. In this formulation, controls, states, and adjoints are viewed as independent variables, the state equation is treated as a constraint. A multilevel Newton method due to Atkinson and Brakhage is applied for its solution. The multilevel Newton method operates on a sequence of grids and uses inexpensive coarse grid information to obtain good approximations for the Newton step. If the coarse grid is sufficiently fine, this yields a fast linearly convergent method which considerably reduces the amount of work per iteration and also requires fewer data to handle. Other advantages of this approach are that the reformulation as a compact fixed point problem yields a decoupling of the phase field model and generates functions that only involve the solution of linear parabolic equations. Numerical examples indicate that the work per iteration of the resulting algorithm is linear in the number of variables, if fast methods for the solution of the linear PDEs are used

ISSN:1055-6788    

DOI:10.1080/10556789708805656

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCR The P*(k)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP

ISSN:1055-6788    

DOI:10.1080/10556789708805657

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The success of interior point algorithms for large-scale linear programming has prompted researchers to extend these algorithms to the semi-definite programming (SDP) case. In this paper, the method of approximate centers of Roos and Vial [14] is extended to SDP. The algorithm is subsequently extended to a primal-dual infeasible start algorithm, by employing a suitable self-dual embedding of the primal-dual SDP problem pair

ISSN:1055-6788    

DOI:10.1080/10556789708805658

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

An iterative method for finding equilibrium points in the case of a smooth convex-concave function and a convex feasible set is proposed. This set is defined by smooth concave functions. The method is based on combining and extending ideas contained in feasible direction methods and relaxation methods for optimization problems and convex inequalities

ISSN:1055-6788    

DOI:10.1080/10556789708805659

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Siram Dasu and Charles Eastman (Eds.): Management of Design: Engineering and Management Perspectives. Kluwer Academic Publishers, Boston/Dordrecht/London, 1994, 277 pages, ISBN: 0-7923-9509-3.

ISSN:1055-6788    

DOI:10.1080/10556789708805660

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789708805654

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor