On the Finiteness of the Criss-Cross Method
نویسندگان
چکیده
In this short paper, we prove the niteness of the criss-cross method by showing a certain binary number of bounded digits associated with each iteration increases monotonically. This new proof immediately suggests the possibility of relaxing the pivoting selection in the criss-cross method without sacri cing the niteness.
منابع مشابه
The finite criss-cross method for hyperbolic programming
In this paper the nite criss-cross method is generalized to solve hyperbolic programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. Finiteness of the procedure is proved under the usual mild assumptions. Some small numerical examples illustrate the main features of the algorithm.
متن کاملThe Linear Complementarity Problem, Sufficient Matrices, and the Criss-Cross Method
Specially structured linear complementarity problems (LCPs) and their solution by the miss-cross method are examined. The criss-cross method is known to be finite for LCPs with positive semidefinite bisymmetric matrices and with P-matrices. It is also a simple finite algorithm for oriented matroid programming problems. Recently Cottle, Pang, and Venkateswaran identified the class of (column, ro...
متن کاملSolving Inequalities and Proving Farkas's Lemma Made Easy
Thus the height of M is exactly 2, as required by (i). The proof of the theorem is complete. ACKNOWLEDGMENTS. I wish to express my warm gratitude to Professor Ram Murty for an interesting discussion that led to the idea of writing this paper. 1. INTRODUCTION. Every college student has learned how to solve a system of linear equations, but how many would know how to solve Ax ≤ b for x ≥ 0 or sho...
متن کاملClosing the gap in pivot methods for linear programming
We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...
متن کاملSome generalizations of the criss-cross method for quadratic programming
Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A nite criss-cross method, based on least{index resolution, is constructed for solving the LCP. In proving nitenes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1989