منابع مشابه
Ellipsoid Method for Linear Programming made simple
In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra.
متن کاملCSC 2411 - Linear Programming and Combinatorial Optimization ∗ Lecture 6 : The Ellipsoid Method
This lecture introduces the Ellipsoid Method, the first polynomialtime algorithm to solve LP. We start by discussing the historical significance of its discovery by L. Khachiyan. Next, we argue that the ability to decide the feasibility of a version of the constraints of an LP is as hard as solving the LP. To gather the intuition behind the Ellipsoid Method, we draw an analogy with a problem of...
متن کاملEllipsoid Method
In this article we give an overview of the Ellipsoid Method. We start with a historic introduction and provide a basic algorithm in Section 2. Techniques to avoid two important assumptions required by this algorithm are considered in Section 2.2. After the discussion of some implementation aspects, we are able to show the polynomial running time of the Ellipsoid Method. The second section is cl...
متن کاملFuzzy Linear Programming Method for Deriving Priorities in the Fuzzy Analytic Hierarchy Process
There are various methods for obtaining the preference vector of pair-wise comparison matrix factors. These methods can be employed when the elements of pair-wise comparison matrix are crisp while they are inefficient for fuzzy elements of pair-wise comparison matrix. In this paper, a method is proposed by which the preference vector of pair-wise comparison matrix elements can be obtained even ...
متن کاملThe Ellipsoid Method: A Survey
In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinari...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1980
ISSN: 0196-8858
DOI: 10.1016/0196-8858(80)90002-0