An easy path to convex analysis and applications

Resource Information

The work An easy path to convex analysis and applications represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

An easy path to convex analysis and applications

Statement of responsibility

Boris S. Mordukhovich, Nguyen Mau Nam

Creator

• Mordukhovich, B. Sh., (Boris Sholimovich)

Contributor

• Nguyen, Mau Nam

Author

• Mordukhovich, B. Sh., (Boris Sholimovich)
• Nguyen, Mau Nam

Subject

• Convex functions
• Convex geometry
• Convex geometry
• Fenchel conjugate
• Fermat-Torricelli problem
• Helly theorem
• MATHEMATICS -- Geometry | General
• Mathematical analysis
• Mathematical analysis
• Nash equilibrium
• Nonsmooth optimization
• Nonsmooth optimization
• Radon theorem
• Weiszfeld algorithm
• convex function
• convex set
• directional derivative
• distance function
• generalized differentiation
• minimal time function
• normal cone
• optimal value function
• optimization
• set-valued mapping
• smallest enclosing ball problem
• subdifferential
• subgradient
• subgradient algorithm
• support function
• Affine set
• Carathéodory theorem
• Convex functions

Language

eng

Summary

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications

Member of

• Synthesis lectures on mathematics and statistics, #14.

Cataloging source

CaBNVSL

Citation source

• Compendex
• INSPEC
• Google scholar
• Google book search

Dewey number

516.08

Illustrations

illustrations

Index

index present

LC call number

QA331.5

LC item number

.M668 2014

Literary form

non fiction

Nature of contents

• dictionaries
• bibliography

Series statement

Synthesis lectures on mathematics and statistics,

Series volume

#14

Target audience

• adult
• specialized