PRACTICAL MATHEMATICAL
OPTIMIZATION
An Introduction to Basic Optimization Theory and
Classical and New Gradient-Based Algorithms
Applied Optimization
VOLUME 97
Series Editors:
Panos M. Pardalos
University of Florida, U.S.A.
Donald W. Heam
University of Fl
J. Frdric Bonnans J. Charles Gilbert
e e
Claude Lemarchal Claudia A. Sagastiz bal
e
a
Numerical Optimization
Theoretical and Practical Aspects
Second Edition
With 52 Figures
J. Frdric Bonnans
e e
J. Charles Gilbert
Centre de Mathmatiques Appliques
e
e
Eco
Paul E. Fishback
Linear and Nonlinear
Programming with Maple:
An Interactive,
Applications-Based Approach
For Barb, Andy, and Margaret
Contents
List of Figures
xiii
List of Tables
xv
Foreword
xix
I Linear Programming
1 An Introduction to Linear Programmin
i
AdvancedOpt-1506 2008/5/14 10:31 page i #1
Notes on Advanced Optimization
Regina S. Burachik
i
AdvancedOpt-1506 2008/5/14 10:31 page ii #2
ii
i
AdvancedOpt-1506 2008/5/14 10:31 page iii #3
Contents
1 Introduction
1.1 Aims of this course . . . . . . . .
Solution to selected problems.
Chapter 1. Preliminaries
1. A FS , t 0, A cfw_T t = (A cfw_S t) cfw_T t, since cfw_T t cfw_S t. Since
A cfw_S t Ft and cfw_T t Ft , A cfw_T t Ft . Thus FS FT .
2. Let = N and F = P(N) be the power set of the natural numbers.
Topic and contents
School of Mathematics and Statistics
MATH3161/MATH5165 Optimization
Prof Jeya Jeyakumar
Topic 09 Optimal Control Theory
1
2
3
Motivation and Examples
Optimal Control Problems
Autonomous systems
MATH3161/MATH5165 (Optimization)
4
5
6
So
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165 OPTIMIZATION Session 1, 2016
Problem Sheet 3 Solutions Convex sets and functions
1. Establish rigorously whether the following sets are convex or not.
(a) = x R2 |
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165 OPTIMIZATION Session 1, 2016
Problem Sheet 7 Line Search Descent Methods
1. Calculate the limits and rates of convergence of the following sequences.
(a) x(k) = ck wh
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165 OPTIMIZATION Session 1, 2016
Problem Sheet 5 Solutions Equality Constraints
2. Consider the equality constrained problem
Minimize x1 + x2 + x3
x R]3
Subject to x21 +
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165 OPTIMIZATION Session 1, 2016
Problem Sheet 2 Solutions Mathematical background
4. Let A be an n by n nonsingular matrix and let G = AT A.
(a) Prove that G is symmetri
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165OPTIMIZATION
CLASS TEST 1 Solutions
Session 1, 2015
(1) TIME ALLOWED 50 Minutes
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF E
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165OPTIMIZATION
CLASS TEST 1
Session 1, 2015
(1) TIME ALLOWED 50 Minutes
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF EQUAL VALUE
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161/MATH5165OPTIMIZATION
CLASS TEST 1
Session 1, 2014
(1) TIME ALLOWED 50 Minutes
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF EQUAL VALUE
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