Numerical Optimization for Applied
Mathematicians
Author: Lok Ming Ronald Lui
Preface:
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.
Contents:
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