Linear programming, the simplex algorithm and simple polytopes
نویسنده
چکیده
In the rst part of the paper we survey some far-reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot rules and upper bounds on the diameter of graphs of polytopes.
منابع مشابه
Linear Programming, the Simplex Algorithm and Simple Polytopes
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
متن کاملSolving multiobjective linear programming problems using ball center of polytopes
Here, we aim to develop a new algorithm for solving a multiobjective linear programming problem. The algorithm is to obtain a solution which approximately meets the decision maker's preferences. It is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution. Numerical examples and a simulation study are used to illu...
متن کاملOne line and n points * Bernd Gärtner † Falk
We analyze a randomized pivoting process involving one line and n points in the plane. The process models the behavior of the Random-Edge simplex algorithm on simple polytopes with n facets in dimension n − 2. We obtain a tight O(log n) bound for the expected number of pivot steps. This is the first nontrivial bound for Random-Edge which goes beyond bounds for specific polytopes. The process it...
متن کاملA new approach to fuzzy quantities ordering based on distance method and its applications for solving fuzzy linear programming
Many ranking methods have been proposed so far. However, there is yet no method that can always give a satisfactory solution to every situation; some are counterintuitive, not discriminating; some use only the local information of fuzzy values; some produce different ranking for the same situation. For overcoming the above problems, we propose a new method for ranking fuzzy quantities based on ...
متن کاملA Proof by the Simplex Method for the Diameter of a (0,1)-Polytope
Naddef [3] shows that the Hirsch conjecture is true for (0,1)-polytopes by proving that the diameter of any (0, 1)-polytope in d-dimensional Euclidean space is at most d. In this short paper, we give a simple proof for the diameter. The proof is based on the number of solutions generated by the simplex method for a linear programming problem. Our work is motivated by Kitahara and Mizuno [2], in...
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:
- Math. Program.
دوره 79 شماره
صفحات -
تاریخ انتشار 1997