Lectures on Convex Sets

By: Valeriu Soltan

Write A Review

eText | 28 November 2019 | Edition Number 2

At a Glance

Format
ePUB

eText

$96.79

or 4 interest-free payments of $24.20 with

Instant online reading in your Booktopia eTextbook Library *

Why choose an eTextbook?

Instant Access *

Purchase and read your book immediately

Read Aloud

Listen and follow along as Bookshelf reads to you

Study Tools

Built-in study tools like highlights and more

* eTextbooks are not downloadable to your eReader or an app and can be accessed via web browsers only. You must be connected to the internet and have no technical issues with your device or browser that could prevent the eTextbook from operating.

The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space. It benefits advanced undergraduate and graduate students with various majors in mathematics, optimization, and operations research. It may be adapted as a primary book or an additional text for any course in convex geometry or convex analysis, aimed at non-geometers. It can be a source for independent study and a reference book for researchers in academia.

The second edition essentially extends and revises the original book. Every chapter is rewritten, with many new theorems, examples, problems, and bibliographical references included. It contains three new chapters and 100 additional problems with solutions.

Contents:

Prerequisites
The Affine Structure of ℝⁿ
Convex Sets
Convex Hulls
Cones and Conic Hulls
Recession Directions
Closedness Conditions
Cone Polarity and Normal Directions
Bounds, Supports, and Asymptotes
Separation Properties
Extreme Structure of Convex Sets
Exposed Structure of Convex Sets
Polyhedra
Solutions to Problems

Readership: Undergraduate and graduate students in mathematics, optimization and operations research. Convex Set;Convex Hull;Cone;Support;Separation;Extreme;Exposed;Polyhedron0Key Features:

The exposition is self-contained, detailed and provides multiple cross-references, that makes the book accessible to a large audience
An essential part of the text is adapted from various research articles, never presented before in a textbook format
The book has a multidisciplinary nature: it can be useful to specialists in geometry, convex analysis, operations research, and optimization
The new edition contains new chapters and additional exercises with respective solutions
Despite the presence of a large number of monographs on convex sets, there are quite a few textbooks on this topic. This book is to the level of graduate study, with higher degree of complexity and essentially more research-related results and references