Lectures on modern convex optimization. Analysis, algorithms, and engineering applications. (English) Zbl 0986.90032

Ben-Tal, Aharon; Nemirovski, Arkadi

MPS/SIAM Series on Optimization 2. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. Philadelphia, PA: MPS, Mathematical Programming Society, xvi, 488 p. (2001).

The book is devoted to well-structured and thus efficiently solvable convex optimization problems, such as linear programming, conic quadratic programming and semidefinite programming. The book consists of 6 lectures. Lecture 1 presents the basic results on the linear programming duality in a form that makes it easy to extend these results to the nonlinear case. Lecture 2 introduces the notion of a conic problem associated with a cone \(K\). Lectures 3 and 4 study two nice generic conic problems of extreme importance: conic quadratic and semidefinite programs. The last two lectures are devoted to the efficiently numerical solution of optimization problems of the studied types. Here the ellipsoid method and an overview of polynomial time-interior-point methods for linear programming, conic quadratic programming and semidefinite programming are presented. Numerous applications in engineering are discussed illustrating the wide spectrum of potential applications of convex optimization. Readers should know the basic facts from linear algebra, analysis and optimization.

Reviewer: Juan Manuel Otero (Habana)

MSC:

90C25	Convex programming
90-02	Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
90C22	Semidefinite programming
90C06	Large-scale problems in mathematical programming

Keywords:

convex programming; conic programming; conic quadratic programming; semidefinite programming; large-scale programming