Modern Optimization Methods / / Qingna LI.

• VerfasserIn: LI, Qingna,
• Place / Publishing House: Les Ulis : : EDP Sciences, , [2023]; 2023
• Year of Publication: 2023
• Language: English
• Physical Description: 1 online resource (157 p.)

With the fast development of big data and artificial intelligence, a natural question is how do we analyze data more efficiently? One of the efficient ways is to use optimization. What is optimization? Optimization exists everywhere. People optimize. As long as you have choices, you do optimization. Optimization is the key of operations research. This book introduces the basic definitions and theory about numerical optimization, including optimality conditions for unconstrained and constrained optimization, as well as algorithms for unconstrained and constrained problems. Moreover, it also includes the nonsmooth Newton's method, which plays an important role in large-scale numerical optimization. Finally, based on the author's research experiences, several latest applications about optimization are introduced, including optimization algorithms for hypergraph matching, support vector machine and bilevel optimization approach for hyperparameter selection in machine learning. With these optimization tools, one can deal with data more efficiently.

Table of Contents

Frontmatter -- Preface -- Contents -- Chapter 1. Introduction -- Chapter 2. Fundamentals of Optimization -- Chapter 3. Line Search Methods -- Chapter 4. Trust Region Methods -- Chapter 5. Conjugate Gradient Methods -- Chapter 6. Semismooth Newton's Method -- Chapter 7. Theory of Constrained Optimization -- Chapter 8. Penalty and Augmented Lagrangian Methods -- Chapter 9. Bilevel Optimization and Its Applications -- Bibliography