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.

Conjugate Duality and Optimization (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 16)

Business & Money

Rockafellar, R. Tyrrell

Economics

Society for Industrial and Applied Mathematics

The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis.
This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Implicit Functions and Solution Mappings: A View from Variational Analysis (Springer Series in Operations Research and Financial Engineering)

Science & Math

Dontchev, Asen L.

Mathematics

Springer

A rigorous and comprehensive treatment of network flow theory and monotropic optimization by one of the world's most renowned applied mathematicians. This classic textbook, first published by J. Wiley &amp; Sons, Inc., in 1984, covers extensively the duality theory and the algorithms of linear and nonlinear network optimization optimization, and their significant extensions to monotropic programming (separable convex constrained optimization problems, including linear programs). Monotropic programming problems are characterized by a rich interplay between combinatorial structure and convexity properties. Rockafellar develops, for the first time, algorithms and a remarkably complete duality theory for these problems.

Network Flows and Monotropic Optimization

Computers & Technology

Certification

Athena Scientific

Variational Analysis (Grundlehren der mathematischen Wissenschaften)

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.

Variational Analysis (Grundlehren der mathematischen Wissenschaften, 317)

Wets, Roger J.-B.

Reference

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Books by Rockafellar, R. Tyrrell