Grippo L. Introduction to Methods for Nonlinear Optimization 2023

Textbook in PDF format

In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems.These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems.The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.
Introduction
Fundamental Definitions and Basic Existence Results
Optimality Conditions for Unconstrained Problems in Rn
Optimality Conditions for Problems with Convex Feasible Set
Optimality Conditions for Nonlinear Programming
Duality Theory
Optimality Conditions Based on Theorems of the Alternative
Basic Concepts on Optimization Algorithms
Unconstrained Optimization Algorithms
Line Search Methods
Gradient Method
Conjugate Direction Methods
Newton’s Method
Trust Region Methods
Quasi-Newton Methods
Methods for Nonlinear Equations
Methods for Least Squares Problems
Methods for Large-Scale Optimization
Derivative-Free Methods for Unconstrained Optimization
Methods for Problems with Convex Feasible Set
Penalty and Augmented Lagrangian Methods
SQP Methods
Introduction to Interior Point Methods
Nonmonotone Methods
Spectral Gradient Methods
Decomposition Methods
Basic Concepts of Linear Algebra and Analysis
Differentiation in Rn
Introduction to Convex Analysis