{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

02 - Industrial Engineering 634 Integer Programming Fall...

This preview shows pages 1–2. Sign up to view the full content.

Industrial Engineering 634 Fall 2011 Integer Programming Lecturer: Nelson Uhan Scribe: Mahesh Ramaraj August 24, 2011 Lecture 2. Linear Programs and Polyhedra Following our discussion on integer programs from last class, we will focus this lecture on linear programs and polyhedra. What is a linear program? Given a matrix A R m × n and vectors b R m and c R n , a linear program is an optimization problem of following form max cx (1) s.t. Ax b (2) Equality constraints can be rewritten as two inequality constraints, and by multiplying by - 1, we can change the direction of the constraints and the objective function. A feasible solution to a linear program of the form (1)-(2) is a vector x such that Ax b . An optimal solution of a linear program of the form (1)-(2) is a feasible solution with maximum value of cx . A linear program of the form (1)-(2) is infeasible if { x R n : Ax b } = and it is unbounded if for all α R , there exists a y ∈ { x R n : Ax b } with cy > α . In rest of the lecture we will focus on the feasible sets of linear programs. A polyhedron in R n is a set of type P = { x R n : Ax b }

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

02 - Industrial Engineering 634 Integer Programming Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online