Lecture 2 : LP Duality , Simplex Method Complexity , Ellipsoid Method

نویسندگان

  • Pankaj K. Agarwal
  • Sam Slee
چکیده

An interesting concept associated with linear programs is that of duality. For every LP problem there is a second LP problem with which it is intrinsically paired. This second LP problem can bound the feasible values of the first problem and even help find the optimal value to that problem. The initial LP problem is called the primal LP while the second is referred to as the dual LP. Consider the example LP problem given below.

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

Linear Programming

This paper is a short didactical introduction to Linear Programming (LP). The main topics are: formulations, notes in convex analysis, geometry of LP, simplex method, duality, ellipsoid algorithm, interior point methods.

متن کامل

CSC 5160 : Combinatorial Optimization and Approximation Algorithms

In this lecture, we will talk about the technique of using Linear Programming (LP) to solve combinatorial optimization problems. The lecture is divided into two parts. In the first part, we discuss the theoretical aspects of LP and illustrate by exmaples how combinatoric problems can be reforumated as LP problems. In the second part, we introduce two popular algorithms in solving LP problems: t...

متن کامل

2 a Quick Review 3 Applications of Duality 3.1 Max-flow = Min-cut

1 Overview In the previous lecture, we introduced several algorithms for solving linear programs, such as simplex algorithm , ellipsoid algorithm, and interior point algorithm. In this lecture, let us look at some typical applications of duality to graph theory. Recall that the primal of a linear program with n variables and m constraints can be written as min c x|Ax ≥ b, x ≥ 0, x ∈ R n The dua...

متن کامل

CSC 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 کامل

Linear Programming

1. Linear Programming Problems 1.1. Formulation of Linear Programming Problems 1.2. Examples 1.3. Different Forms of Programs and Transformations 2. Primal and Dual Programs and Polyhedra 2.1 Duality 2.2. Linear Inequalities and Polyhedra 3. The Simplex Method 3.1. The Restriction-oriented Simplex Method 3.2. The Variable-oriented Simplex Method 3.3. Modifications of Methods and Problems 3.4. T...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007