Numerical Optimization for Applied Mathematicians

   Lok Ming Ronald Lui

Optimization refers to a process of selecting the best element within an admission set which minimizes some sorts of functionals. It has been widely used in various research fields in applied mathematics, such as image processing, medical image analysis and shape analysis. Because of its importance, numerical optimization is considered as the prerequisite for researchers in applied mathematics. This book is intended to give a concise overview of different numerical optimization techniques. It is hoped that the book can help junior researchers to grasp the basic idea of the topic for their scietific research. The book is written as simple as possible. It comes with exercises and projects of practical applications. Solutions of the exercises will be given upon request.


Chapter 1: Introduction

Chapter 2: Fundamentals of Numerical Optimization

Chapter 3: Basics of Unconstrained Optimization Problems

Chapter 4: Newton's method

Chapter 5: Quasi-Newton method

Chapter 6: Conjugate gradient method

Chapter 7: Non-linear least square problem

Chapter 8: Basics of Constrained Optimization

Chapter 9: The Simplex method

Chapter 10: Interior Point Method

Chapter 11: Penalty, Barrier and Augmented Lagrangian Methods

Chapter 12: Non-linear Constrained Optimization Problems