附註:Includes bibliographical references (pages 255-258) and index.
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.
摘要:"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
