Optimization / Kenneth Lange.
Material type:
TextSeries: Publication details: New York : Springer, 2013.Edition: 2nd edDescription: xvii, 529 p. : ill. ; 24 cmISBN: - 9781461458371 (alk. paper)
- 519.3 23 L274
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 519.3 L274 (Browse shelf(Opens below)) | Available | 135860 |
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| 519.3 L111 Simulated annealing | 519.3 L222 Advanced mathematics for economicsts static and dynamic optimization | 519.3 L274 Optimization | 519.3 L274 Optimization / | 519.3 L418 Combinatorial optimization | 519.3 L478 First course in combinatorial optimization | 519.3 L533 Topics of optimization |
Includes bibliographical references (p. 499-518) and index.
1. Elementary optimization --
2. The seven c's of analysis --
3. The gauge integral --
4. Differentiation --
5. Karush-Kuhn-Tucker theory --
6. Convexity --
7. Block relaxation --
8. The MM algorithm --
9. The EM algorithm --
10. Newton's method and scoring --
11. Conjugate gradient and quasi-Newton --
12. Analysis of convergence --
13. Penalty and barrier methods --
14. Convex calculus --
15. Feasibility and duality --
16. Convex minimization algorithms --
17. The calculus of variations --
Appendix--
References--
Index.
Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition, the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.
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