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Convex Optimization & Euclidean Distance Geometry By Jon Dattorro
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Optimization is the science of making a best choice in the face of conflicting requirements. Any convex optimization problem has geometric interpretation. If a given optimization problem can be... More > transformed to a convex equivalent, then this interpretive benefit is acquired. That is a powerful attraction: the ability to visualize geometry of an optimization problem. Conversely, recent advances in geometry hold convex optimization within their proofs' core. This book is about convex optimization, convex geometry (with particular attention to distance geometry), geometrical problems, and problems that can be transformed into geometrical problems. Euclidean distance geometry is, fundamentally, a determination of point conformation from interpoint distance information; e.g., given only distance information, determine whether there corresponds a realizable configuration of points; a list of points in some dimension that attains the given interpoint distances. 2005 International Edition I< Less
Convex Optimization & Euclidean Distance Geometry By Jon Dattorro
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Convex Analysis is the calculus of inequalities while Convex Optimization is its application. Analysis is inherently the domain of the mathematician while Optimization belongs to the engineer. In... More > layman’s terms, the mathematical science of Optimization is the study of how to make a good choice when confronted with conflicting requirements. The qualifier Convex means: when an optimal solution is found, then it is guaranteed to be a best solution; there is no better choice. As any Convex Optimization problem has geometric interpretation, this book is about convex geometry (with particular attention to distance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convex problems. A virtual flood of new applications follows by epiphany that many problems, presumed nonconvex, can be so transformed. Revised & Enlarged International Paperback Edition III< Less