v2004.06.19 - Convex Optimization

Chapter 1PreludePeople are so afraid of convex analysis.−Claude Lemaréchal, 2003Convex Analysis is the calculus of inequalities while Convex Optimizationis its application. Analysis is inherently the domain of the mathematicianwhile Optimization belongs to the engineer. It can be difficult for the engineerto apply theory without understanding Analysis. Boyd & Vandenberghe’sbook Convex Optimization [1] is a marvelous bridge between the two disciplines;rigorous though accessible to non-mathematicians. Their text wasconventionally published in 2004 having been taught at Stanford Universityand made freely available on the world-wide web for ten prior years; 1.1 adissemination motivated by the belief that a virtual flood of new applicationswould follow by epiphany that many problems hitherto presumednon-convex could be transformed or relaxed into convexity. [2] [3] [4] [5] [6][7, §4.3, p.316-322] [8] [9] [10] Subsequently there were great advances, particularlyin the electronic circuit design industry. [7, §4.7] [11] [12]-[21]1.0 c○ 2001 Jon Dattorro, all rights reserved.1.1 Its influence has already great impact; the web holds countless copies in bits and piecesspanning the book’s evolution.15