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Convex Optimization & Euclidean Distance Geometry Southern Politics HeÕs evidence that if youConvex 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 laymans 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