Introduction to the Theory of Optimization in Euclidean Space
Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications.
Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations.
Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses.
- Rigorous and practical, offering proofs and applications of theorems
- Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers
- Introduces complex principles in a clear, illustrative fashion
1.1. Formulation of some optimization problems
1.2. Particular subsets of Rn
1.3. Functions of several variables
2. Unconstrained Optimization
2.1. Necessary condition
2.2. Classification of local extreme points
2.3. Convexity/concavity and global extreme points
2.4. Extreme value theorem
3. Constrained Optimization-Equality constraints
3.1. Tangent plane
3.2. Necessary condition for local extreme points-Equality constraints
3.3. Classification of local extreme points-Equality constraints
3.4. Global extreme points-Equality constraints
4. Constrained Optimization-Inequality constraints
4.1. Cone of feasible directions
4.2. Necessary condition for local extreme points/Inequality constraints
4.3. Classification of local extreme points-Inequality constraints
4.4. Global extreme points-Inequality constraints
4.5. Dependence on parameters
"This book fills in the gap between the advanced, theoretical books on abstract Hilbert spaces, and the more practical books intended for Engineers, where theorems lack proofs. The author presents many theorems, along with their proofs, in a simple way and provides many examples and graphical illustrations to allow students grasp the material in an easy and quick way."
—Professor Salim Aissa Salah Messaoudi, University of Sharjah, UAE