MA4254: Discrete Optimization
Additional LP used material in Chapter 3
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NU
MA4254: Discrete Optimization
Additional LP used material in Chapter 3
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2015
(Based on notes by Prof Sun Defeng)
NU
MA4254: Discrete Optimization
Example on Branch and Bound
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1/
MA4254: Discrete Optimization
Chapter 3: The Shortest Path
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1
MA4254: Discrete Optimization
Additional LP used material in Chapter 3
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2015
(Based on notes by Prof Sun Defeng)
NU
MA4254: Discrete Optimization
Chapter 1: Introduction
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1/61
A
Simplex Method (Shortened version for MA4254)
A tableau implements the simplex method conveniently.
From now on, we'll use tableaus for computation and analysis.
A generic simplex tableau is as follow
MA4254: Discrete Optimization
Chapter 4: The Greedy Algorithm and Computational
Complexity
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2015
(Based on notes by
MA4254: Discrete Optimization
Chapter 5: Algorithms for N PC
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254:
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Date: 23 Oct 2015 (Fri)
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NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 4
Q1. Refer to the Primal-Dual Algorithm in the lecture notes.
(a) Show that eve
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 3
Solution or hint to selected questions
Q1. [Outline of proof: We start with th
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 1
Solution to selected questions
Q1.
n
n
min
cij xij
i=1 j=1
n
xij = 1,
i = 1, ,
MA4254: Discrete Optimization
Chapter 3: The Shortest Path
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1
MA4254: Discrete Optimization
Chapter 2: Total Unimodularity and its applications
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun
MA4254: Discrete Optimization
Chapter 4: The Greedy Algorithm and Computational
Complexity
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by
MA4254: Discrete Optimization
Chapter 3: The Shortest Path
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1
MA4254: Discrete Optimization
Chapter 1: Introduction
Pang Chin How Jerey
Department of Mathematics
National University of Singapore
August 2014
(Based on notes by Prof Sun Defeng)
NUS: MA4254: 1/61
A
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 2
Q1. Prove, for a given graph G = (V, E), that the following are equivalent:
(i
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 1
Q1. Suppose that there are n people and n jobs. Each job must be assigned to e
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 3
Q1. Suppose that A Rmn is of full row rank (m n), c, d Zm and c < d. Show that
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
Semester I (2014/2015) MA4254 Discrete Optimization Tutorial 2
Solution or hint to selected questions
Q1. Recall that a tree is a connected a