Math 407 Linear Optimization 1
1.1
Introduction
What is optimization?
A mathematical optimization problem is one in which some function is either maximized or minimized relative to a given set of alternatives. The function to be minimized or maximized is
1
1.1
Solving LPs: The Simplex Algorithm of George Dantzig
Simplex Pivoting: Dictionary Format
We illustrate a general solution procedure, called the simplex algorithm, by implementing it on a very simple example. Consider the LP (1.1) max 5x1 + 4x2 + 3x3
Outline Course Mechanics Linear Algebra Review Block Structured Matrices Gaussian Elimination Matrices Gauss-Jordan El
Math 407A: Linear Optimization
Professor James Burke
Math Dept, University of Washington
June 22, 2010
Professor James Burke Math 407A:
LP Modeling
Model 10: Detergent Production
Model 9: Investing Over Time
Math 407A: Linear Optimization
Lecture 3: LP Modeling
Math Dept, University of Washington
Lecture 3: LP Modeling: Math 407A: Linear Optimization
Math Dept, University of Washington
LP
Outline LPs in Standard Form Minimization maximization Linear equations to linear inequalities Lower and upper bounded
Math 407A: Linear Optimization
Lecture 4: LP Standard Form
Math Dept, University of Washington
Lecture 4: LP Standard Form Math 407A: Li
Outline Dictionaries, Augmented Matrices, the Simplex Tableau Basic Feasible Solutions (BFS) The Grand Strategy: Pivoting Th
Math 407A: Linear Optimization
Lecture 5: Simplex Algorithm I
Math Dept, University of Washington
Lecture 5: Simplex Algorithm I: