Algorithms for Optimization (Hardcover)

Mykel J. Kochenderfer , Tim A. Wheeler

買這商品的人也買了...

商品描述

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems.

This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language.

Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

商品描述(中文翻譯)

這本書是一本全面介紹優化的書籍,重點放在設計工程系統的實用演算法上。

這本書提供了一個全面的優化介紹,重點放在實用演算法上。書籍從工程的角度來處理優化問題,目標是設計一個系統,以優化一組指標並滿足限制條件。讀者將學習各種計算方法,包括在高維空間中搜索、處理存在多個競爭目標的問題以及處理指標不確定性的方法。圖片、例子和練習題傳達了數學方法背後的直覺。本書提供了在Julia程式語言中的具體實現。

涵蓋的主題包括導數及其在多維空間中的推廣;局部下降法和一階和二階方法,這些方法對局部下降法提供了信息;隨機方法,將隨機性引入優化過程;線性約束優化,當目標函數和約束條件都是線性時;替代模型、概率替代模型以及使用概率替代模型指導優化;不確定性下的優化;不確定性傳播;表達式優化;以及多學科設計優化。附錄提供了Julia語言的介紹、用於評估演算法性能的測試函數以及在本書中討論的優化方法的推導和分析所使用的數學概念。本書可供高年級本科生和研究生在數學、統計學、計算機科學、任何工程領域(包括電氣工程和航空航天工程)以及運籌學中使用,也可作為專業人士的參考資料。