Optimization

The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes graduate students in applied mathematics, computational biology, computer science, economics, and physics as well as upper division undergraduate majors in mathematics who want to see rigorous mathematics combined with real applications.

Chapter 1 reviews classical methods for the exact solution of optimization problems. Chapters 2 and 3 summarize relevant concepts from mathematical analysis. Chapter 4 presents the Karush-Kuhn-Tucker conditions for optimal points in constrained nonlinear programming. Chapter 5 discusses convexity and its implications in optimization. Chapters 6 and 7 introduce the MM and the EM algorithms widely used in statistics. Chapters 8 and 9 discuss Newton’s method and its offshoots, quasi-Newton algorithms and the method of conjugate gradients. Chapter 10 summarizes convergence results, and Chapter 11 briefly surveys convex programming, duality, and Dykstra’s algorithm.

From the reviews:

"...An excellent, imaginative, and authoritative text on the difficult topic of modeling the problems of multivariate outcomes with different scaling levels, different units of analysis, and differentstudy designs simultaneously." Biometrics, March 2005

"...As a textbook, Optimization does provide a valuable introduction to an important branch of applicable mathematics." Technometrics, August 2005

"...I found Optimization to be an extremely engaging textbook....the text is ideal for graduate students or researchers beginning research on optimization problems in statistics. There is little doubt that someone who worked through the text as part of a reading course or specialized graduate seminar would benefit greatly from the author's perspective..." Journal of the American Statistical Association, December 2005