Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (MPS-SIAM Series on Optimization)

(Here is a book devoted to well-structured and thus effici...)

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.

http://www.amazon.com/gp/product/0898714915/?tag=2022091-20

Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (MPS-SIAM Series on Optimization) by Aharon Ben-Tal (2001-08-01)

http://www.amazon.com/gp/product/B01NANDFLA/?tag=2022091-20

Robust Optimization (Princeton Series in Applied Mathematics)

( Robust optimization is still a relatively new approach ...)

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

http://www.amazon.com/gp/product/0691143684/?tag=2022091-20