|
Showing 1 - 3 of
3 matches in All Departments
This volume is based on lectures delivered at the 2019 AMS Short
Course ""Sum of Squares: Theory and Applications'', held January
14-15, 2019, in Baltimore, Maryland. This book provides a concise
state-of-the-art overview of the theory and applications of
polynomials that are sums of squares. This is an exciting and
timely topic, with rich connections to many areas of mathematics,
including polynomial and semidefinite optimization, real and convex
algebraic geometry, and theoretical computer science. The six
chapters introduce and survey recent developments in this area;
specific topics include the algebraic and geometric aspects of sums
of squares and spectrahedra, lifted representations of convex sets,
and the algorithmic and computational implications of viewing sums
of squares as a meta algorithm. The book also showcases practical
applications of the techniques across a variety of areas, including
control theory, statistics, finance and machine learning.
This book provides a self-contained, accessible introduction to the
mathematical advances and challenges resulting from the use of
semidefinite programming in polynomial optimization. This important
and highly applicable research area with contributions from convex
geometry, algebraic geometry, and optimization is known as convex
algebraic geometry. Each chapter addresses a fundamental aspect of
the topic, beginning with an introduction to nonnegative
polynomials and sums of squares, and their connections to
semidefinite programming. The material quickly advances to areas at
the forefront of current research, including semidefinite
representability of convex sets, duality theory in algebraic
geometry, and nontraditional topics such as sums of squares of
complex forms. The book is a suitable entry point to the subject
for readers at the graduate level or above in mathematics,
engineering or computer science. Instructors will find the book
appropriate for a class or seminar, and researchers will encounter
open problems and new research directions.
This book presents a course in the geometry of convex polytopes in
arbitrary dimension, suitable for an advanced undergraduate or
beginning graduate student. The book starts with the basics of
polytope theory. Schlegel and Gale diagrams are introduced as
geometric tools to visualize polytopes in high dimension and to
unearth bizarre phenomena in polytopes. The heart of the book is a
treatment of the secondary polytope of a point configuration and
its connections to the state polytope of the toric ideal defined by
the configuration. These polytopes are relatively recent constructs
with numerous connections to discrete geometry, classical algebraic
geometry, symplectic geometry, and combinatorics.The connections
rely on Grobner bases of toric ideals and other methods from
commutative algebra. The book is self-contained and does not
require any background beyond basic linear algebra. With numerous
figures and exercises, it can be used as a textbook for courses on
geometric, combinatorial, and computational aspects of the theory
of polytopes.
|
You may like...
The Hidden
Fiona Snyckers
Paperback
R340
R266
Discovery Miles 2 660
Katvis
Annelie Botes
Paperback
R320
R250
Discovery Miles 2 500
The Murder Inn
James Patterson, Candice Fox
Paperback
R365
R260
Discovery Miles 2 600
Crosshairs
James Patterson, James O Born
Paperback
R380
R297
Discovery Miles 2 970
The Kill List
Nadine Matheson
Paperback
R410
R275
Discovery Miles 2 750
The Survivors
Jane Harper
Paperback
R459
R380
Discovery Miles 3 800
Shadow State
Andy McNab
Paperback
R335
R268
Discovery Miles 2 680
Never
Ken Follett
Paperback
R375
R293
Discovery Miles 2 930
|