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Nonlinear optimization with financial applications / Michael Bartholomew-Biggs

Main Author Bartholomew-Biggs, Michael C. Country Estados Unidos. Publication Boston : Kluwer, cop. 2005 Description IX, 261 p. ; 25 cm ISBN 1-4020-8110-3 CDU 519.853
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Holdings
Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca Geral da Universidade do Minho
BGUMD 109915 Available 370215
Monografia Biblioteca Geral da Universidade do Minho
BGUMD 109914 Available 384713
Total holds: 0

Enhanced descriptions from Syndetics:

This instructive book introduces the key ideas behind practical nonlinear optimization, accompanied by computational examples and supporting software. It combines computational finance with an important class of numerical techniques.

Table of contents provided by Syndetics

  • List of Figures
  • List of Tables
  • Preface
  • 1 Portfolio Optimization
  • 1 Nonlinear optimization
  • 2 Portfolio return and risk
  • 3 Optimizing two-asset portfolios
  • 4 Minimimum risk for three-asset portfolios
  • 5 Two- and three-asset minimum-risk solutions
  • 6 A derivation of the minimum risk problem
  • 7 Maximum return problems
  • 2 One-Variable Optimization
  • 1 Optimality conditions
  • 2 The bisection method
  • 3 The secant method
  • 4 The Newton method
  • 5 Methods using quadratic or cubic interpolation
  • 6 Solving maximum-return problems
  • 3 Optimal Portfolios With N Assets
  • 1 Introduction
  • 2 The basic minimum-risk problem
  • 3 Minimum risk for specified return
  • 4 The maximum return problem
  • 4 Unconstrained Optimization in N Variables
  • 1 Optimality conditions
  • 2 Visualising problems in several variables
  • 3 Direct search methods
  • 4 Optimization software and examples
  • 5 The Steepest Descent Method
  • 1 Introduction
  • 2 Line searches
  • 3 Convergence of the steepest descent method
  • 4 Numerical results with steepest descent
  • 5 Wolfe''s convergence theorem
  • 6 Further results with steepest descent
  • 6 The Newton Method
  • 1 Quadratic models and the Newton step
  • 2 Positive definiteness and Cholesky factors
  • 3 Advantages and drawbacks of Newton''s method
  • 4 Search directions from indefinite Hessians
  • 4 Numerical results with quasi-Newton methods
  • 5 Numerical results with the Newton method
  • 7 Quasinewton Methods
  • 1 Approximate second derivative information
  • 2 Rauk-two updates for the inverse Hessian
  • 3 Convergence of quasi-Newton methods
  • 5 The rank-one update for the inverse Hessian
  • 6 Updating estimates of the Hessian
  • 8 Conjugate Gradient Methods
  • 1 Conjugate gradients and quadratic functions
  • 2 Conjugate gradients and general functions
  • 3 Convergence of conjugate gradient methods
  • 4 Numerical results with conjugate gradients
  • 5 The truncated Newton method
  • 9 Optimal Portfolios With Restrictions
  • 1 Introduction
  • 2 Transformations to exclude short-selling
  • 3 Results from Minrisk2u and Maxret2u
  • 4 Upper and lower limits on invested fractions
  • 10 Larger-Scale Portfolios
  • 1 Introduction
  • 2 Portfolios with increasing numbers of assets
  • 1 Data fitting problems
  • 3 Time-variation of optimal portfolios
  • 4 Performance of optimized portfolios
  • 11 Data-Fitting And The Gauss-Newton Method
  • 2 The Gauss-Newton method
  • 3 Least-squares in time series analysis
  • 4 Gauss-Newton applied to time series
  • 5 Least-squares forms of minimum-risk problems
  • 6 Gauss-Newton applied to Minrisk1 and Minrisk 2
  • 12 Equality Constrained Optimization
  • 1 Portfolio problems with equality constraints
  • 2 Optimality conditions
  • 3 A worked example
  • 4 Interpretation of Lagrange multipliers
  • 5 Some example problems
  • 13 Linear Equality Constraints
  • 1 Equality constrained quadratic programming
  • 2 Solving minimum-risk problems as EQPs
  • 3 Reduced-gradient methods
  • 4 Projected gradient methods
  • 5 Results with methods for linear constraints
  • 14 Penalty Function Methods
  • 1 Introduction
  • 2 Penalty functions
  • 3 The Augmented Lagrangian
  • 1 Introduction
  • 4 Results with P-SUMT and AL-SUMT
  • 5 Exact penalty functions
  • 15 Sequential Quadratic Programming
  • 2 Quadratic/linear models
  • 3 SQP methods based on penalty functions
  • 4 Results with AL-SQP
  • 5 SQP line searches and the Maratos effect
  • 16 Further Portfolio Problems
  • 1 Including transaction costs
  • 2 A re-balancing problem
  • 3 A sensitivity problem
  • 17 Inequality Constrained Optimization
  • 1 Portfolio problems with inequality constraints
  • 2 Optimality conditions
  • 3 Transforming inequalities to equalities
  • 4 Transforming inequalities to simple bounds
  • 5 Example problems
  • 18 Extending Equality-Constraint Methods
  • 1 Inequality constrained quadratic programming
  • 2 Reduced gradients for inequality constraints
  • 3 Penalty functions for inequality constraints
  • 4 AL-SUMT for inequality constraints
  • 5 SQP for inequality constraints
  • 6 Results with P-SUMT, AL-SUMT and AL-SQP
  • 19 Barrier Function Methods
  • 1 Introduction
  • 2 Barrier functions
  • 3 Numerical results with B-SUMT
  • 20 Interior Point Methods
  • 1 Introduction
  • 2 Approximate solutions of problem B-NLP
  • 3 An interior p

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