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Convex Analysis
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions. This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
Variational Analysis
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Conjugate Duality and Optimization
Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
Convex Analysis and Optimization
A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a ...
Lectures on the Coupling Method
Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
The Physics and Chemistry of Mineral Surfaces
The last two decades have brought a near exponential increase in the amount known about mineral surfaces. Get a handle on this overwhelming mountain of information with The Physics and Chemistry of Mineral Surfaces. This much-needed text will save you hours of tedious journal searches by providing an excellent condensation and overview of the entire field, including its future direction. Top researchers outline atomistic controls on mineral surface structure and reactions; apply these concepts to explain sorption, mineral corrosion and growth; and ultimately consider the role of surfaces in environmental and geochemical processes. This unique text provides a rich and rigorous treatment of th...
Biology and the Mechanics of the Wave-Swept Environment
This text introduces and draws together pertinent aspects of fluid dynamics, physical oceanography, solid mechanics, and organismal biology to provide a much-needed set of tools for quantitatively examining the biological effects of ocean waves. "Nowhere on earth does water move as violently as on wave-swept coasts," writes the author, "and every breaker that comes pounding on the shore places large hydrodynamic forces on the organisms resident there." Yet wave-swept coral reefs and rocky shores are home to some of the world's most diverse assemblages of plants and animals, and scientists have chosen these environments to carry out much of the recent experimental work in community structure ...
Optical Microcavities
Optical microcavities are structures that enable confinement of light to microscale volumes. The universal importance of these structures has made them indispensable to a wide range of fields. This important book describes the many applications and the related physics, providing both a review and a tutorial of key subjects by leading researchers from each field. The topics include cavity QED and quantum information, nanophotonics and nanostructure interactions, wavelength switching and modulation in optical communications, optical chaos and biosensors.
Princeton Guide to Advanced Physics
From classical mechanics to general relativity, the key principles in all areas of physics are surveyed in this one handy volume. Here Alan Tribble addresses the needs of students and practicing physicists alike. He starts with a review of mathematical methods and then summarizes the most widely used concepts in physics, detailing derivations and applications. With its mix of theory, application, and solved problems, Advanced Physics enables a student to grasp quickly the fundamentals of the field while providing physicists, engineers, and mathematicians with an ideal reference for locating critical formulas or reviewing mathematical details. One of Tribble's goals is to help students, parti...
Geometry of Nonpositively Curved Manifolds
Starting from the foundations, the author presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two. The book builds to a discussion of the Mostow Rigidity Theorem and its generalizations, and concludes by exploring the relationship in nonpositively curved spaces between geometric and algebraic properties of the fundamental group. This introduction to the geometry of symmetric spaces of non-compact type will serve as an excellent guide for graduate students new to the material, and will also be a useful reference text for mathematicians already familiar with the subject.
