摘要:

Hausdorff distance between solution sets of original and perturbed linear inequalities systems in real partially ordered Banach space is estimated. The estimation receives a particular simple expression for finite dimensional case. The concept of condition number for solution set of a linear inequalities system is suggested. Explicit expressions of Lipschitz constants are given

ISSN:1055-6788    

DOI:10.1080/10556789508805622

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

This paper represents a truncated dual sequential quadratic programming method with limited memory, which can solve sparse and dense large-scale nonlinear programming problems. Because an approximation of the inverse Hessian matrix of the Lagrangian function is formulated in a dual quadratic programming subproblem with simple bounds, the computation of the inverse matrix in the subproblem is avoided. A truncated solution of the dual quadratic programming subproblem is determined by an iterative method, in which the computation of the matrix-vector product, instead of the matrix factorization, is needed such that the implementation at each iteration is relatively simple and time-economic. With the technique of a limited memory update, the estimated inverse Hessian matrix of the Lagrangian function is computed and stored by means of some vectors, and this decreases the computation in solving the dual quadratic programming subproblem. The global convergence of the algorithm is proved and the numerical results on small and large test problems are given

ISSN:1055-6788    

DOI:10.1080/10556789508805623

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

A quadratically convergent line-search algorithm for piecewise smooth convex optimization based on a discontinuous piecewise linear approximation of the subgradient of the objective function is proposed. The algorithm safeguards the optimal point and has a global linear rate of convergence with locally quadratic convergence in the case of an isolated non-degenerate kink at the solution. For practical purposes it can be combined with the line-search routine based on cubic approximation of the objective function to produce an algorithm suitable for both smooth and nonsmooth optimization

ISSN:1055-6788    

DOI:10.1080/10556789508805624

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789508805625

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789508805621

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor