摘要:

Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and efficient. Both algorithms are based on transforming the problem to one with constraints over the cone of positive semidefinite matrices, i.e. Löwner order constraints. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row

ISSN:1055-6788    

DOI:10.1080/10556789508805599

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this paper, we consider the application of the optimally stable ABS subclass to nonlinear underdetermined systems. By a similar approach to that in [4], we convert this subclass into an approximate normal flow algorithm [5,6]. Using such equivalent variation, the semilocal convergence of the new methods is established

ISSN:1055-6788    

DOI:10.1080/10556789508805600

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

This paper describes two algorithms for the problem of minimizing a linear function over the intersection of an affine set and a convex set which is required to be the closure of the domain of a strongly self-concordant Barrier function. One algorithm is a path-following methods while the other is a primal potential-reduction method. We give bounds on the number of iterations necessary to attain a given accuracy

ISSN:1055-6788    

DOI:10.1080/10556789508805601

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this paper, we present a new method for minimizing a convex quadratic function of many variables with box constraints. The new algorithm is a modification of a method introduced recently by Friedlander and Martinez {SIAM J. on Optimization, February 1994). Following the lines of More and Toraldo (SIAM J. on Optimization 1, pp. 93-113), it combines an efficient unconstrained method with gradient projection techniques. The strategy for “leaving the current face” makes it possible to obtain convergence even when the Hessian is singular. Dual nondegeneracy is not assumed anywhere. The unconstrained minimization algorithm used within the faces was introduced by Barzilai and Borwein and analyzed by Raydan (IMA Journal of Numerical Analysis13, pp. 321-326)

ISSN:1055-6788    

DOI:10.1080/10556789508805602

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this article we present a simple introduction to the notion of self-concordance and its implications for convex programming. We consider certain interior-point methods for solving convex programs

ISSN:1055-6788    

DOI:10.1080/10556789508805603

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Among the most interesting methods for finding the minimizer of a functionf{x) of several variables when gradients are available, are conic-variable metric methods [1,4,11,12]. Much of the published theory only studies the local convergence properties of this class, save that a global convergence theorem depending on exact line searches is given in [5].In practice, it is best to be quite tolerant in the termination criterion of line searches. Therefore, this paper studies the global convergence of this method with inexact line searches. It is shown that, if /f(x) is uniformly convex, then convergence to the minimizer is obtained, and the rate of convergence is superlinear. Moreover, we prove the convergence of a more general variable metric method with two parameters proposed by Spedicato [13]

ISSN:1055-6788    

DOI:10.1080/10556789508805604

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789508805598

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor