v2010.10.26 - Convex Optimization

Chapter 1OverviewConvex OptimizationEuclidean Distance GeometryPeople are so afraid of convex analysis.−Claude Lemaréchal, 2003In layman’s terms, the mathematical science of Optimization is the studyof how to make a good choice when confronted with conflicting requirements.The qualifier convex means: when an optimal solution is found, then it isguaranteed to be a best solution; there is no better choice.Any convex optimization problem has geometric interpretation. If a givenoptimization problem can be transformed to a convex equivalent, then thisinterpretive benefit is acquired. That is a powerful attraction: the ability tovisualize geometry of an optimization problem. Conversely, recent advancesin geometry and in graph theory hold convex optimization within their proofs’core. [394] [319]This book is about convex optimization, convex geometry (withparticular attention to distance geometry), and nonconvex, combinatorial,and geometrical problems that can be relaxed or transformed into convexproblems. A virtual flood of new applications follows by epiphany that manyproblems, presumed nonconvex, can be so transformed. [10] [11] [59] [93][149] [151] [277] [298] [306] [361] [362] [391] [394] [34,4.3, p.316-322]2001 Jon Dattorro. co&edg version 2010.10.26. All rights reserved.citation: Dattorro, Convex Optimization & Euclidean Distance Geometry,Mεβoo Publishing USA, 2005, v2010.10.26.21