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- 2012948598 abstract "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 -- Source other than Library of Congress.".
- 2012948598 contributor B12704450.
- 2012948598 created "c2013.".
- 2012948598 date "2013".
- 2012948598 date "c2013.".
- 2012948598 dateCopyrighted "c2013.".
- 2012948598 description "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.".
- 2012948598 description "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 -- Source other than Library of Congress.".
- 2012948598 description "Includes bibliographical references (p. 499-518) and index.".
- 2012948598 extent "xvii, 529 p. :".
- 2012948598 identifier "1461458374 (alk. paper)".
- 2012948598 identifier "9781461458371 (alk. paper)".
- 2012948598 identifier "9781461458388 (ebk.)".
- 2012948598 isPartOf "Springer texts in statistics ; 95.".
- 2012948598 isPartOf "Springer texts in statistics, 1431-875X ; 95".
- 2012948598 issued "2013".
- 2012948598 issued "c2013.".
- 2012948598 language "eng".
- 2012948598 publisher "New York : Springer,".
- 2012948598 subject "519.6 22".
- 2012948598 subject "Mathematical optimization.".
- 2012948598 subject "QA402.5 .L34 2013".
- 2012948598 tableOfContents "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.".
- 2012948598 title "Optimization / Kenneth Lange.".
- 2012948598 type "text".