Nonlinear Optimization with Financial Applications

• Main Author: Bartholomew-Biggs, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2005.
• Subjects: Mathematics.; Finance.; Numerical analysis.; Computer mathematics.; Mathematical optimization.; Operations research.; Management science.; Optimization.; Operations Research, Management Science.; Numeric Computing.; Computational Mathematics and Numerical Analysis.; Finance, general.; Numerical Analysis.

• The book introduces the key ideas behind practical nonlinear optimization. • Computational finance—an increasingly popular area of mathematics degree programmes—is combined here with the study of an important class of numerical techniques. • The financial content of the book is designed to be rel...

Table of Contents:

• Portfolio Optimization
• One-Variable Optimization
• Optimal Portfolios with N Assets
• Unconstrained Optimization in N Variables
• The Steepest Descent Method
• The Newton Method
• Quasi-Newton Methods
• Conjugate Gradient Methods
• Optimal Portfolios with Restrictions
• Larger-Scale Portfolios
• Data-Fitting & The Gauss-Newton Method
• Equality Constrained Optimization
• Linear Equality Constraints
• Penalty Function Methods
• Sequential Quadratic Programming
• Further Portfolio Problems
• Inequality Constrained Optimization
• Extending Equality-Constraint Methods to Inequalities
• Barrier Function Methods
• Interior Point Methods
• Data Fitting Using Inequality Constraints
• Portfolio Re-Balancing and other Problems
• Global Unconstrained Optimization.