IE 534 Linear Programming
Lecture 3: Linear programming formulation
Lizhi Wang
August 24, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
August 24, 2012
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Outline
1
Review
2
General form LP
3
Standard form LP
Lizhi Wang ([email protected]
IE 534 Linear Programming
Lecture 20: Benders Decomposition (2)
Lizhi Wang
October 8, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 8, 2012
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Outline
1
Algorithm
2
McDonald Example
Lizhi Wang ([email protected])
IE 534 Linea
IE 534 Linear Programming
Lecture 21: Sensitivity Analysis
Lizhi Wang
October 22, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
1 / 30
Outline
1
Motivation
2
Gusek for sensitivity analysis
3
Four cases of sensitivity anal
IE 534 Linear Programming
Lecture 22: Sensitivity Analysis (2)
Lizhi Wang
October 24, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 24, 2012
1 / 14
Case 1: c c + c
Changing the objective coefcients could possibly affect dual
feasi
IE 534 Linear Programming
Lecture 23: Multi-objective Optimization
Lizhi Wang
October 26, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 26, 2012
1 / 18
Motivation
We may have more than one objective to optimize
maximize prot, qual
IE 534 Linear Programming
Lecture 26: Integer Linear Programming
Branch and Bound
Lizhi Wang
November 2, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
November 2, 2012
1 / 30
Outline
1
Denitions
2
Demonstration
3
Algorithm
4
Example
Lizh
IE 534 Linear Programming
Lecture 29: Bilevel Linear Programming
Lizhi Wang
November 9, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
November 9, 2012
1 / 28
Bilevel linear program
A bilevel linear program (BLP) can be written as
max
x,y
IE 534 Linear Programming Homework 3
Student name: Chintan Prajapati
Instructor name: Lizhi Wang
Date assigned: Wednesday 10/12/2016
Date due: Monday 10/24/2016, 5:00 PM
Homework must be submitted as a single pdf document by email to [email protected]
IE 534 Linear Programming Homework 1
Instructor name: Lizhi Wang
Student name: Abdullah Alnaqeb
Date assigned: Friday 09/02/2016
Date due: Wednesday 09/14/2016, 5:00 PM
Homework must be submitted as a single pdf document by email to [email protected]
IE 534 Linear Programming Homework 5
Student name: Chintan Prajapati
Instructor name: Lizhi Wang
Date assigned: Friday 11/11/2016
Date due: Friday 11/18/2016, 5:00 PM
Homework must be submitted as a single pdf document by email to [email protected]
H
IE 534 Linear Programming
Lecture 17: Dual Simplex
Lizhi Wang
October 1, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 1, 2012
1 / 13
Primal dictionary
maxx cfw_ = c x : Ax b, x 0.
maxx,w cfw_ = c x : Ax + w = b, x 0, w 0.
maxx cf
IE 534 Linear Programming
Lecture 16: The Simplex Algorithm (6)
Lizhi Wang
September 28, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 28, 2012
1 / 16
Outline
1
Review
2
Is the Simplex algorithm guaranteed to terminate nitely?
3
IE 534 Linear Programming
Lecture 15: The Simplex Algorithm (5)
Lizhi Wang
September 26, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 26, 2012
1 / 20
Outline
1
Review
2
How to check the unboundedness of an LP?
3
How to nd a bet
IE 534 Linear Programming
Lecture 2: Introduction to Linear Programming
Lizhi Wang
August 22, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
August 22, 2012
1 / 11
Outline
1
Two Crude Petroleum
2
Graphical method
Lizhi Wang ([email protected]
IE 534 Linear Programming
Lecture 4: Computer solvers
Lizhi Wang
August 27, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
August 27, 2012
1 / 21
Outline
1
Integer and nonlinear programming examples
2
Matlab for LP and QP
3
Gusek for LP an
IE 534 Linear Programming
Lecture 5: Modeling (I)
Lizhi Wang
August 29, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
August 29, 2012
1 / 17
Outline
1
Review
2
Arbitrage in currency exchange
3
Turning junk into treasure
4
Old McDonald had
IE 534 Linear Programming
Lecture 6: Modeling (II)
Lizhi Wang
September 5, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 5, 2012
1 / 30
Outline
1
Review
2
Minimizing a convex piecewise linear objective function
3
Dealing with bi
IE 534 Linear Programming
Lecture 7: Optimality Condition
Lizhi Wang
September 7, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 7, 2012
1 / 18
Outline
1
Announcement and Review
2
Optimality Condition
Lizhi Wang ([email protected]
IE 534 Linear Programming
Lecture 8: LP Duality
Lizhi Wang
September 10, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 10, 2012
1 / 22
Outline
1
Review
2
Optimality condition of standard form LP
3
Optimality condition of non-sta
IE 534 Linear Programming
Lecture 10: Farkas Lemma
Lizhi Wang
September 14, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 14, 2012
1/8
Outline
1
Farkas lemma
2
Primal-dual possibilities
Lizhi Wang ([email protected])
IE 534 Lin
IE 534 Linear Programming
Lecture 11: The Simplex Algorithm (1)
Lizhi Wang
September 17, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 17, 2012
1 / 17
Outline
1
Homework 3
2
Simplex algorithm overview
3
What exactly is a corner
IE 534 Linear Programming
Lecture 12: The Simplex Algorithm (2)
Lizhi Wang
September 19, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 19, 2012
1 / 15
Outline
1
Review
2
Is the optimal solution always basic?
3
How to nd a basic
IE 534 Linear Programming
Lecture 13: The Simplex Algorithm (3)
Lizhi Wang
September 21, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 21, 2012
1 / 12
Outline
1
Review
2
How to nd a fbp to start from?
Lizhi Wang ([email protected]
IE 534 Linear Programming
Lecture 14: The Simplex Algorithm (4)
Lizhi Wang
September 24, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
September 24, 2012
1 / 30
Outline
1
Review
2
How to check the optimality of a fbp?
3
How to check the u
IE 534 Linear Programming
Lecture 1: Course Overview
Lizhi Wang
August 20, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
August 20, 2012
1 / 26
Outline
1
Ice breaker
2
What linear programming is about
3
What linear programming can do
4
Lo