Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
By addebook • Nov 15th, 2008 • Category: Mathematics •
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Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (MPS-SIAM Series on Optimization)
by Aharon Ben-Tal, Arkadi Nemirovski
Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (MPS-SIAM Series on Optimization)
By Aharon Ben-Tal, Arkadi Nemirovski
Publisher: Society for Industrial Mathematics
Number Of Pages: 488
Publication Date: 2001-08-01
ISBN-10 / ASIN: 0898714915
ISBN-13 / EAN: 9780898714913
Binding: Paperback
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book’s focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Summary: A good reference source for convex optimization
Rating: 4
Lectures on Convex Optimization is devoted to well structured
and efficiently solvable convex optimization problems, with
an emphasis on conic quadratic and semidefinite programming.
The authors begin with linear programming, and then progress
to conic programming. [I really enjoyed their description
of the transition from linear to general conic
programming!]. They then discuss two special conic
optimization problems namely second order cone programming,
and semidefinite programming. Numerous applications of conic
programming espcially in filter design, Lyapunov stability
analysis, and structural design are presented. The book concludes with
a discussion on the computational tractability of convex
programs, and primal dual interior point algorithms to
solving general conic optimization problems.
One can then take on the likes of Renegar’s recent book
on interior point methods, and
Nesterov and Nemirovski’s seminal treatise on the general
theory of interior point methods in convex optimization,
at a more advanced level.
My only minor comments are :-
(a) The organization of the book as a series of 6 lectures
is misleading, since there is quite a lot of material
covered in each lecture.
(b) The book has a very short [almost
nonexistent] bibliography.
All in all, a good workout and an encyclopedic source for
anyone interested in theory and applications of convex
optimization. Highly recommended!.
Summary: A good reference source for convex optimization
Rating: 4
Lectures on Convex Optimization is devoted to well structured
and efficiently solvable convex optimization problems, with
an emphasis on conic quadratic and semidefinite programming.
The authors begin with linear programming, and then progress
to conic programming. [I really enjoyed their description
of the transition from linear to general conic
programming!]. They then discuss two special conic
optimization problems namely second order cone programming,
and semidefinite programming. Numerous applications of conic
programming espcially in filter design, Lyapunov stability
analysis, and structural design are presented. The book concludes with
a discussion on the computational tractability of convex
programs, and primal dual interior point algorithms to
solving general conic optimization problems.
One can then take on the likes of Renegar’s recent book
on interior point methods, and
Nesterov and Nemirovski’s seminal treatise on the general
theory of interior point methods in convex optimization,
at a more advanced level.
My only minor comments are :-
(a) The organization of the book as a series of 6 lectures
is misleading, since there is quite a lot of material
covered in each lecture.
(b) The book has a very short [almost
nonexistent] bibliography.
All in all, a good workout and an encyclopedic source for
anyone interested in theory and applications of convex
optimization. Highly recommended!.
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