摘要:

Interior point methods that follow the primal-dual central path of a dual pair of linear programs (Po),(Do) require that these problems are strictly feasible. To get around this difficulty, one technique is to embed (Po),(Do) into a family of suitably perturbed strictly feasible linear programs (Pr),(Dr),r>0and to follow the path (x(r),s(r)),r>0, of all strictly feasible solutions of (Pr),(Dr) withxi(r)si(r)=r,i= 1…,n. Path following methods compute approximations to this path at parametersR=ro>r1>…, and their complexity is measured by the numberN=N(r, R) of steps needed to reduce a givenR>0 to a desiredr>0. It is shown for a standard method thatN(r, R) is estimated by a boundwhereCois a universal constant but K=K(ƀ,ȼ)is a constant depending ƀ,ȼ on with K(0,0)=0, and on the sizeof the path.

ISSN:1055-6788    

DOI:10.1080/10556789408805552

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper we establish theq-uadratic convergence rate of a local Newton-like method for equality constrained minimization problems. We also consider a wide class of differentiable exact penalty functions and show that, in principle, they can be used to globalize the local algorithm without destroying its fast convergence rate.

ISSN:1055-6788    

DOI:10.1080/10556789408805553

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

A single linear program is proposed for discriminating between the elements of κ disjoint point sets in then-dimensional real spaceRn. When the conical hulls of the κ sets are (κ−1)-point disjoint inRn+1, a κ-piece piecewise-linear surface generated by the linear program completely separates the κ sets. This improves on a previous linear programming approach which required that each set be linearly separable from the remaining κ−1 sets. When the conical hulls of the κ sets are not (κ;−1)-point disjoint, the proposed linear program generates an error-minimizing piecewise-linear separator for the κ Sets. For this case it is shown that the null solution is never a unique solver of the linear program and occurs only under the rather rare condition when the mean of each point set equals the mean of the means of the other κ−l sets. This makes the proposed linear computational programming formulation useful for approximately discriminating between κ sets that are not piecewise-linear separable. Computational results are reported for three previously available databases.

ISSN:1055-6788    

DOI:10.1080/10556789408805554

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, we present a new kind of ABS methods, called row update ABS methods, for solving systems of nonlinear equations. We use the previous function values to approximate derivatives of functions in some sense. Onlyncomponent function evaluations at each iteration are needed and no derivatives of functions are involved. Under some mild assumptions, we prove that the row update ABS methods are locally and superlinearly convergent. A numerical comparison with Newton's method, Brqyden's method and the original ABS methods is also given, showing that the new methods are competitive with other methods. AMS Subject Classification:65H10

ISSN:1055-6788    

DOI:10.1080/10556789408805555

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Interval arithmetic algorithms A.l and A.2 that determine computationally rigorous bounds on the global minimizers of continuous functionswithout inequality constraints and with inequality constraintsrespectively are described. It is assumed that, for A.land that forand. Computational experience indicates that A.l and A.2 always succeed, although in some cases more than one interval containing a global minimizer is found. Numerical results obtained from Sun Pascal implementations of A.l and A.2 are presented.

ISSN:1055-6788    

DOI:10.1080/10556789408805556

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this work we present convergence conditions for iterative methods, expressed in terms of a vector performance criterion. Moreover, we propose a constructive scheme for enforcing global convergence based on these conditions and we discuss some applications to stabilization of optimization algorithms.

ISSN:1055-6788    

DOI:10.1080/10556789408805557

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

This paper presents some more numerical experiments with LSNNO, a new FORTRAN subroutine for solving large-scale nonlinear network optimization problems. The implemented algorithm applies the concepts of partial separability and partitioned quasi-Newton updating to high-dimensional nonlinear network optimization problems. The experiments reported involve both academic and practical problems.

ISSN:1055-6788    

DOI:10.1080/10556789408805558

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper we present a new sequential algorithm for solving one-dimensional and multidimensional (using Peano-type space filling curves for reduction of the dimensionality) multiextremal global optimization problems. A parallel version of the algorithm is also described. Sufficient conditions for global convergence are proved for both the methods. Numerical experiments are also presented.

ISSN:1055-6788    

DOI:10.1080/10556789408805559

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

A new iterative algorithm for solving unconstrained optimization problems is introduced. It is based on the construction, at each iteration, of a curvilinear path to be searched for a local solution. Since the curvilinear path is denned by using a tensor of third order partial derivatives of the objective function, efficient and reliable implementations can benefit of powerful computational tools like parallel computing and automatic differentiation. Computational experiments were carried out with the aim to compare the proposed algorithm with well known Newton type algorithms. It turns out that the proposed algorithm is very efficient especially in the case of badly scaled and ill-conditioned problems.

ISSN:1055-6788    

DOI:10.1080/10556789408805560

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper we present a general approach for treating first order approximation schemes constrained extremum problems. We underline that, roughly speaking, these schemes present two geometric one and an analytical one. We will show that separation theorems and tangent fundamental role for deriving a scheme from the geometrical viewpoint; from the other derivative is the key concept for the analytical viewpoint. The purpose of the paper is scheme for first order approximations in optimization and to put in evidence the connections geometrical and analytical properties of the problem. The main interest is devoted to those which are useful for deriving necessary optimality conditions and for the construction of Solution methods.

ISSN:1055-6788    

DOI:10.1080/10556789408805561

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor