New variants of finite criss-cross pivot algorithms for linear programming

نویسنده

  • Shuzhong Zhang
چکیده

In this paper we generalize the so called rst in last out pivot rule and the most often selected variable pivot rule for the simplex method as proposed in Zhang to the criss cross pivot setting where neither the primal nor the dual feasibility is preserved The nite ness of the new criss cross pivot variants is proven

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A New Admissible Pivot Method for Linear Programming

We present a new admissible pivot method for linear programming that works with a sequence of improving primal feasible interior points and dual feasible interior points. This method is a practicable variant of the short admissible pivot sequence algorithm, which was suggested by Fukuda and Terlaky. Here, we also show that this method can be modified to terminate in finite pivot steps. Finedly,...

متن کامل

Criss-cross methods: A fresh view on pivot algorithms

This paper surveys the origins and implications of ( nite) criss-cross methods in linear programming and related problems. Most pivot algorithms, like Dantzig's celebrated Simplex method, need a feasible basis to start with; when the basis is changed, feasibility is preserved until optimality or unboundedness is detected. To obtain a feasible basis a so-called rst phase problem must be solved. ...

متن کامل

The s-monotone index selection rules for pivot algorithms of linear programming

In this paper we introduce the concept of s-monotone index selection rule for linear programming problems. We show that several known anticycling pivot rules like the minimal index-, last-in-first-outand themost-often-selected-variable pivot rules are s-monotone index selection rules. Furthermore, we show a possible way to define new s-monotone pivot rules. We prove that several known algorithm...

متن کامل

On Anti-cycling Pivoting Rules for the Simplex Method, Operations the Equivalence of Dantzig's Self-dual Parametric Algorithm for Linear Programs to Lemke's Algorithm for Linear Complementarity Problems Applied to Linear Programming, Technical Report

Rotterdam 9707/A (1997). 82] S. Zionts, The criss-cross method for solving linear programming problems, English title: A new, nite criss-cross method for solving linear programming problems.) 64] T. Terlaky, A convergent criss-cross method, Math. Oper. und Stat. ser. Some generalizations of the criss-cross method for the linear complementarity problem of oriented matroids, Combinatorica 9 23] G...

متن کامل

Some 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • European Journal of Operational Research

دوره 116  شماره 

صفحات  -

تاریخ انتشار 1999