摘要:

In this paper a comprehensive theory is attempted of methods of conjugate-gradient type where the matrix of coefficients may be definite, indefinite or nonsymmetric. The theory is based on ‘leveling’ some underlying quadratic function over a linear manifold rather than just a straight line. It is shown that numerical instabilites occur when this quadratic Hessian is indefinite (well-known) or when another matrix employed, often implicitly, in the calculations is indefinite. The use of the various ‘look-ahead’ algorithms in combatting these instabilities is outlined and it is seen that this amounts to a ‘sequential block’ method. It is further shown that many well-known algorithms have ‘simultaneous block’ versions, where the size and composition of the initial blocks are essentially arbitrary. Since the columns of the individual blocks may be generated simultaneously rather than sequentially these methods lend themselves naturally to the techniques of parallel computation.

ISSN:1055-6788    

DOI:10.1080/10556789308805531

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper we analyze the conjugate gradient method when the objective function is quadratic. We apply backward analyses to study the quadratic termination of the conjugate gradient method. Forward analyses are used to derive some properties of the conjugate gradient method, including the only linear convergence of the method and an upper bound for the rate of convergence.

ISSN:1055-6788    

DOI:10.1080/10556789308805532

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

An implementable method for nonsmooth multiobjective optimization is described. The algorithm is a modification of the well-known Geoffrion-Dyer-Feinberg (GDF) method for smooth interactive multiobjective problems. The smooth gradient-based Frank-Wolfe method exploited in the GDF method is replaced by a modified (Kiev) subgradient method in order to compute the search direction. The solutions are projected onto the set of Pareto optimal points by using exact penalty scalarizing functions. A bundle-type method is utilized to solve the nonsmooth single objective optimization problems arising in every iteration of the procedure.

ISSN:1055-6788    

DOI:10.1080/10556789308805533

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper we propose an easy-to-implement algorithm for solving general nonlinear optimization problems with nonlinear equality constraints. In order to deal with large scale problems, a reduced Hessian is used to replace full Hessian matrix. To avoid solving quadratic trust region subproblems exactly, which usually takes most computing time, we only require an approximate solution with less computation. The calculation of correction steps, that is necessary from theoretical view point to overcome Maratos effect but often brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. Global convergence and a local superlinear rate are then proved. Numerical results are reported to show that this algorithm has good performance.

ISSN:1055-6788    

DOI:10.1080/10556789308805534

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

A linear program is said to be improper if its feasible set is empty or its optimal value is infinite. Improper programs appear as the result of inaccurate information, excessive simplification, considering some restrictions as unchangeable, etc. Moreover, a contradictory model may fit the real contradictions adequately, and the ways of transforming it into a noncontradictory one (the ways of correcting it) may correspond to real procedures for solving these contradictions. The paper describes the DELTA-PLAN-ES interactive system for numerical analysis of improper linear programs. The system is designed for Rjad-2 ES computers.

ISSN:1055-6788    

DOI:10.1080/10556789308805535

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789308805530

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor