Titlebook: Convex Analysis for Optimization; A Unified Approach Jan Brinkhuis Textbook 2020 Springer Nature Switzerland AG 2020 Convex set.Convex func

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Convex Sets: Topological Properties,: this is needed for work with unbounded convex sets. Here is an example of the use of recession directions: they can turn ‘non-existence’ (of a bound for a convex set or of an optimal solution for a convex optimization problem) into existence (of a recession direction). This gives a certificate for

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Convex Sets: Dual Description,which a closed proper convex set can be described: from the inside, by its points (‘primal description’), and from the outside, by the halfspaces that contain it (‘dual description’). Applications of duality include the theorems of the alternative: non-existence of a solution for a system of linear

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Convex Functions: Dual Description,e (constant plus linear) functions, has to be investigated. This has to be done for its own sake and as a preparation for the duality theory of convex optimization problems. An illustration of the power of duality is the following task, which is challenging without duality but easy if you use dualit

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Convex Problems: The Main Questions,problems. It is necessary to have theoretical tools to solve these problems. Finding optimal solutions exactly or by means of a law that characterizes them, is possible for a small minority of problems, but this minority contains very interesting problems. Therefore, most problems have to be solved

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Optimality Conditions: Reformulations, (KKT) conditions, the minimax and saddle point theorem, Fenchel duality. Therefore, it is important to know what they are and how they are related..? What..– Duality theory. To a convex optimization problem, one can often associate a concave optimization problem with a completely different variable

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Application to Convex Problems,ill illustrate all theoretical concepts and results in this book. This phenomenon is in the spirit of the quote by Cervantes. Enjoy watching the frying of eggs in this chapter and then fry some eggs yourself!.? What. In this chapter, the following problems are solved completely; in brackets the tech

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