Coverart for item
The Resource Nonlinear optimization with financial applications, Michael Bartholomew-Biggs

Nonlinear optimization with financial applications, Michael Bartholomew-Biggs

Label
Nonlinear optimization with financial applications
Title
Nonlinear optimization with financial applications
Statement of responsibility
Michael Bartholomew-Biggs
Creator
Subject
Language
eng
Summary
"The book is aimed at lecturers and students (undergraduate and postgraduate) in mathematics, computational finance and related subjects. It is also useful for researchers and practitioners who need a good introduction to nonlinear optimization."--Jacket
Is part of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Bartholomew-Biggs, Michael C
Dewey number
519.7/6
Illustrations
illustrations
Index
index present
Language note
English
LC call number
T57.8
LC item number
.B37 2005eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Nonlinear programming
  • Mathematical optimization
  • Programmation non linéaire
  • Optimisation mathématique
  • MATHEMATICS
  • Mathematical optimization
  • Nonlinear programming
  • Mathematical optimization
  • Nonlinear programming
  • Optimaliseren
  • Otimização matemática
  • Programação não linear
Label
Nonlinear optimization with financial applications, Michael Bartholomew-Biggs
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 255-258) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover -- Table of Contents -- 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 & 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 & drawbacks of Newton's method -- 4 Search directions from indefinite Hessians -- 5 Numerical results with the Newton method -- 7. QUASI-NEWTON METHODS -- 1 Approximate second derivative information -- 2 Rank-two updates for the inverse Hessian -- 3 Convergence of quasi-Newton methods -- 4 Numerical results with 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 -- 3 Time-variation of optimal portfolios -- 4 Performance of optimized portfolios -- 11. DATA-FITTING & THE GAUSS-NEWTON METHOD -- 1 Data fitting problems -- 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 & Minrisk2 -- 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
Control code
262680129
Dimensions
unknown
Extent
1 online resource (xvii, 261 pages)
Form of item
online
Isbn
9781280190438
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b102601
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4020-8110-1
Specific material designation
remote
System control number
(OCoLC)262680129
Label
Nonlinear optimization with financial applications, Michael Bartholomew-Biggs
Publication
Bibliography note
Includes bibliographical references (pages 255-258) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Cover -- Table of Contents -- 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 & 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 & drawbacks of Newton's method -- 4 Search directions from indefinite Hessians -- 5 Numerical results with the Newton method -- 7. QUASI-NEWTON METHODS -- 1 Approximate second derivative information -- 2 Rank-two updates for the inverse Hessian -- 3 Convergence of quasi-Newton methods -- 4 Numerical results with 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 -- 3 Time-variation of optimal portfolios -- 4 Performance of optimized portfolios -- 11. DATA-FITTING & THE GAUSS-NEWTON METHOD -- 1 Data fitting problems -- 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 & Minrisk2 -- 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
Control code
262680129
Dimensions
unknown
Extent
1 online resource (xvii, 261 pages)
Form of item
online
Isbn
9781280190438
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/b102601
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4020-8110-1
Specific material designation
remote
System control number
(OCoLC)262680129

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      38.944491 -92.326012
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