v2010.10.26 - Convex Optimization

Appendix CSome analytical optimal resultsPeople have been working on Optimization since the ancientGreeks [Zenodorus, circa 200bc] learned that a string enclosesthe most area when it is formed into the shape of a circle.−Roman PolyakWe speculate that optimization problems possessing analytical solutionhave convex transformation or constructive global optimality conditions,perhaps yet unknown; e.g.,7.1.4, (1700),C.3.0.1.C.1 Properties of infimainf ∅ ∞(1677)sup ∅ −∞Given f(x) : X →R defined on arbitrary set X [199,0.1.2]inf f(x) = − sup −f(x)x∈X x∈Xsupx∈Xf(x) = −infx∈X −f(x) (1678)arg inf f(x) = arg sup −f(x)x∈X x∈Xarg supx∈Xf(x) = arg infx∈X −f(x) (1679)2001 Jon Dattorro. co&edg version 2010.10.26. All rights reserved.citation: Dattorro, Convex Optimization & Euclidean Distance Geometry,Mεβoo Publishing USA, 2005, v2010.10.26.653