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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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發(fā)表于 2025-3-21 18:50:02 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Convex Analysis for Optimization
副標(biāo)題A Unified Approach
編輯Jan Brinkhuis
視頻videohttp://file.papertrans.cn/238/237833/237833.mp4
概述Presents a unified novel three-step method for all constructions, formulas and proofs of the important classic notions of convexity.Includes numerous exercises and illustrations to stimulate learning
叢書(shū)名稱Graduate Texts in Operations Research
圖書(shū)封面Titlebook: Convex Analysis for Optimization; A Unified Approach Jan Brinkhuis Textbook 2020 Springer Nature Switzerland AG 2020 Convex set.Convex func
描述.This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization..The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use..".The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching.."? .Shuzhong Zhang., Professor of Industrial and Systems Engineering,
出版日期Textbook 2020
關(guān)鍵詞Convex set; Convex function; Convex optimization problem; Recession cone; Convex duality; Convex cone; Con
版次1
doihttps://doi.org/10.1007/978-3-030-41804-5
isbn_softcover978-3-030-41806-9
isbn_ebook978-3-030-41804-5Series ISSN 2662-6012 Series E-ISSN 2662-6020
issn_series 2662-6012
copyrightSpringer Nature Switzerland AG 2020
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 22:15:22 | 只看該作者
板凳
發(fā)表于 2025-3-22 01:27:49 | 只看該作者
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
地板
發(fā)表于 2025-3-22 07:28:48 | 只看該作者
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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發(fā)表于 2025-3-22 09:59:20 | 只看該作者
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發(fā)表于 2025-3-22 13:59:32 | 只看該作者
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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發(fā)表于 2025-3-22 20:06:34 | 只看該作者
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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發(fā)表于 2025-3-22 23:13:05 | 只看該作者
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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發(fā)表于 2025-3-23 05:07:18 | 只看該作者
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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發(fā)表于 2025-3-23 08:55:24 | 只看該作者
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