摘要:

This paper reviews development in ABS methods following the first international ABS conference, held in Luoyang, September 1991

ISSN:1055-6788    

DOI:10.1080/10556789708805668

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We describe an algorithm of the ABS class, which solves a general qonsingular linear system inn3/3 + 0(n2) multiplications without the assumption that the coefficient matrix be regular. The method can be viewed as a variation of the implicit LU algorithm of the ABS class, whose associated factorization contains a factor which is not triangular (but can be reduced to triangular form after suitable row permutations). We describe king the Abaffan properties of the method, including in particular an efficient way of upd matrix after column interchanges. Such a problem arises in the application to the simplex algorithm, where the implicit LX algorithm provides a faster technique than the standard LU factorization for the pivoting operation if the number of equality constraints m is greater thann/2

ISSN:1055-6788    

DOI:10.1080/10556789708805669

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The symmetric ABS method is considered for solving matrix equations. A remarkable feature of this method is that, for a given matrix equation, it provides a Solution in closed form that has interesting least change properties. This result is exploited to establish secant-type updates by solving certain least change problems. Both Broyden's updates for nonlinear systems of equations and the weak secant updates for unconstrained optimization proposed by Dennis and Wolkowicz are extended to the multiple case

ISSN:1055-6788    

DOI:10.1080/10556789708805670

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper, we discuss the application of the ABS algorithm to the simplex method, the dual simplex method, the linear complementary problem. We consider the ABS formulation of the stopping criterion, the search direction, the minimal rule to determine the vectors entering and leaving the basis matrix and the updating of the Abaffian matrix after a basis vector exchange. The Lemke algorithm for the LCP problem is reformulated in terms of the ABS procedure

ISSN:1055-6788    

DOI:10.1080/10556789708805671

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper the ABS algorithm with singular initial matrix is considered and used to construct an active set algorithm for solving the linear programming prbblem. We prove that this active set algorithm is reduced to the simplex algorithm whep it starts from a vertex or it meets a vertex

ISSN:1055-6788    

DOI:10.1080/10556789708805672

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

This paper considers solving the convex quadratic programming problem. We solve the quadratic programming problem with only equality constraints by ail ABS approach, using the active set strategy. The computational cost of some of the proposed algorithms is considerably less than the cost of classical recommended methods

ISSN:1055-6788    

DOI:10.1080/10556789708805673

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

A tentatively complete bibliography of ABS methods up to the end containing 303 entries. pf 1996 is given

ISSN:1055-6788    

DOI:10.1080/10556789708805674

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789708805667

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor