Optimization
 Author/Creator
 Lange, Kenneth.
 Language
 English.
 Imprint
 2nd ed.  New York : Springer, c2013.
 Physical description
 xvii, 529 p. : ill. ; 24 cm.
 Series
 Springer texts in statistics ; 95.
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 499518) and index.
 Contents

 1. Elementary optimization
 2. The seven c's of analysis
 3. The gauge integral
 4. Differentiation
 5. KarushKuhnTucker theory
 6. Convexity
 7. Block relaxation
 8. The MM algorithm
 9. The EM algorithm
 10. Newton's method and scoring
 11. Conjugate gradient and quasiNewton
 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.
 Summary
 Finitedimensional 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 finitedimensional 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.
Subjects
 Subject
 Mathematical optimization.
Bibliographic information
 Publication date
 2013
 Responsibility
 Kenneth Lange.
 Series
 Springer texts in statistics ; 95
 ISBN
 9781461458371
 1461458374
 9781461458388
 1461458382