Nonlinear optimization with financial applications非线性优化以财政应用
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作者： Michael Bartholomew-Biggs著
出 版 社： 化学工业出版社
出版时间： 2005-1-1字数：版次：页数： 261印刷时间： 2005/01/01开本： 16开印次：纸张： 胶版纸I S B N ： 9781402081101包装： 精装内容简介
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.
目录
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
