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Optimization
ISBN-13:
9781461458388
Veröffentl:
2013
Seiten:
529
Autor:
Kenneth Lange
Serie:
95, Springer Texts in Statistics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
Elementary Optimization.- The Seven C's of Analysis.- The Gauge Integral.- Differentiation.- Karush-Kuhn-Tucker Theory.- Convexity.- Block Relaxation.- The MM Algorithm.- The EM Algorithm.- Newton's Method and Scoring.- Conjugate Gradient and Quasi-Newton.- Analysis of Convergence.- Penalty and Barrier Methods.- Convex Calculus.- Feasibility and Duality.- Convex Minimization Algorithms.- The Calculus of Variations.- Appendix: Mathematical Notes.- References.- Index.
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