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Linear Optimisation and Numerical Analysis
MX3503
Ian Craw
Foreword
What the Course Tries to Do
Aims
Learning Outcomes
The Course
Syllabus
These Notes
The Web Version
The MX3503 Mailing List
Computer Algebra Systems
Books
Tutorials
Acknowledgements
Contents
Introducing the Simplex Algorithm
Constrained Optimisation
Some Sample Problems
Maximising a Function of Two Variables with Constraints
Machine Shop Scheduling
A Transport Problem
A Blending Problem
A More Elaborate Example
Linear Programming Problems
Standard form
A Preview
An Example
Improving the Solution
Questions
1
The One-phase Simplex Algorithm
Solutions of Systems of Linear Equations
Basic Solutions
Row-equivalent matrices
Computation of basic solutions
Change of basis
Return to the Linear Programming Problem
The One-phase Simplex Algorithm
A partial proof
Questions
2
Using Maple
Getting Access to Maple
Using Maple in a PC Classroom
Running M
APLE
on sysa
Saving your work
Printing From Maple
Using Maple to Check Results
Pivoting Using Maple
Cycling in Example 2.26
An Extended Exercise
The Two-Phase Simplex Algorithm
Introduction
The Second Phase Described
Artificial Variables
The
M
method
Another Example
Minimising with the Big
M
Method
A Partial Proof
Avoiding Non-Negativity
An Alternative View
Questions
3
Duality
Formulation of the Dual
The Fundamental Theorem
Shadow Prices
The Dual Simplex Method
Questions
4
The Theory of Games
Matrix Games
Pure strategies
Mixed Strategies
The Fundamental Theorem
Questions
5
Non-linear Optimisation Problems
Relaxing linearity conditions
Maxima and Minima
Lagrange's Principle
Inequality Constraints
Convexity
Questions
6
Genetic Optimisation
A Simple Algorithm
Coding the Domain
Genetic algorithms: process model
Variations
Further Discussion
The Travelling Salesman Problem
Linear Programming Formulation
Genetic Algorithm Formulation
Example Problems
Numerical Optimisation
Credit Card Scoring
Designing FGGA's
The Cocktail Party Effect
Mondrians
Prisoners Dilemma
Multiple Objective Functions
Simulated Annealing
Introduction
Overview
An Example - the Travelling Salesman Problem
Coding
Re-arrangements
Objective Function
Annealing Schedule
Minimising a Function
Comparison
Questions
7
Solutions to Exercises
Solutions for Questions
1
Solutions for Questions
2
Solutions for Questions
3
Solutions for Questions
4
Solutions for Questions
5
Solutions for Questions
6
Solutions for Questions
7
Bibliography
Index
About this document ...
Ian Craw 2002-09-11
