Nonlinear optimization with financial applications非线性优化以财政应用 pdf 在线 2025 epub 免费 书籍 下载

The book introduces the key ideas behind practical nonlinear optimization. Computational finance – an increasingly popular area of mathematics degree programs – is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material – which occupies about one-third of the text – is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performance is demonstrated on a range of optimization problems arising in financial mathematics. Theoretical convergence properties of methods are stated, and formal proofs are provided in enough cases to be instructive rather than overwhelming. Practical behavior of methods is illustrated by computational examples and discussions of efficiency, accuracy and computational costs. Supporting software for the examples and exercises is available (but the text does not require the reader to use or understand these particular codes). The author has been active in optimization for over thirty years in algorithm development and application and in teaching and research supervision.

1.PORTFOLIO OPTIMIZATION

2.ONE-VARIABLE OPTIMIZATION

3.OPTIMAL PORTFOLIOS WITH N ASSETS

4.UNCONSTRAINED OPTIMIZATION IN N VARIABLES

5.THE STEEPEST DESCENT METHOD

6.THE NEWTON METHOD

7.QUASI-NEWTON METHODS

8.CONJUGATE GRADIENT METHODS

9.OPTIMALPORTFOLISO WITH RESTRICTIONS

10.LARGER-SCALE PORTFOLIOS

11.DATA-FITTING & THE GAUSS-NEWTON METHOD

12.EQUALITY CONSTRSINED OPTIMIZATION

13.LINEAR EQUALITY CONSTRAINTS

14.PENALTY FUNCTION METHODS

15.SEQUENTIAL QUADRATIC PROGRAMMING

16.FURTHER PORTFOLIO PROBLEMS

17.INEQUALITY CONSTRAINED OPTIMIZATION

18.EXTENDING EQUALITY-CONSTRAINT METHODS

19.BARRIER FUNCTION METHODS

20.INTERIOR POINT METHODS

21.DATA FITTING USING INEQUALITY CONSTRAINTS

22.PORTFOLIO RE-BALANCING AND OTHER PROBLEMS

23. GLOBAL UNCONSTRAINED OPTIMIZATION

Appendix

References

Index

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《Nonlinear Optimization with Financial Applications非线性优化以财政应用》内容简介:The book introduces the key ideas behind practical nonlinear optimization. Computational finance – an increasingly popular area of mathematics degree programs – is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material – which occupies about one-third of the text – is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performance is demonstrated on a range of optimization problems arising in financial mathematics. Theoretical convergence properties of methods are stated, and formal proofs are provided in enough cases to be instructive rather than overwhelming. Practical behavior of methods is illustrated by computational examples and discussions of efficiency, accuracy and computational costs. Supporting software for the examples and exercises is available (but the text does not require the reader to use or understand these particular codes). The author has been active in optimization for over thirty years in algorithm development and application and in teaching and research supervision.