This textbook is based on lectures given by the authors at MIPT (Moscow), HSE (Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all, the authors focused on the program of a two-semester course of lectures on convex optimization, which is given to students of MIPT. The first chapter of this book contains the materials of the first semester ("Fundamentals of convex analysis and optimization"), the second and third chapters contain the materials of the second semester ("Numerical methods of convex optimization"). The textbook has a number of features. First, in contrast to the classic manuals, this book does not provide proofs of all the theorems mentioned. This allowed, on one side, to describe more themes, but on the other side, made the presentation less self-sufficient. The second important point is that part of the material is advanced and is published in the Russian educational literature, apparently for the first time. Third, the accents that are given do not always coincide with the generally accepted accents in the textbooks that are now popular. First of all, we talk about a sufficiently advanced presentation of conic optimization, including robust optimization, as a vivid demonstration of the capabilities of modern convex analysis.
翻译:本教科书以作者们在下列机构的演讲为基础:MIPT(莫斯科)、HSE(莫斯科)、FEFU(弗拉迪沃斯托克)、V.I.Vernadsky KFU(Simferopol)、AsU(Adygea共和国)和Grenoble-Alpes大学(法国格列诺布尔)。首先,作者们侧重于关于Convex优化的两期课程的节目。首先,作者们侧重于关于Convex优化的两期课程的节目,提供给MIPT的学生。本书第一章载有第一学期的材料(“Convex分析与优化的基本原理”)、第二和第三章载有第二学期的材料(“Numerical comvex优化方法”)、AsUniversity-Alpeles大学(法国格列诺布尔)。首先,与经典的手册不同,这本书没有提供上述所有主题的证明。一方面,给MIPT学生们描述更多的主题,另一方面,使演示变得不那么自足。第二重要的一点是,现在关于材料精度的演示部分是关于精度的演示,我们读的第三阶段的文字的深度,我们读的深度的深度的文字是完全的深度,我们所读的深度的深度的深度的文字,我们所读的文字是完全的深度的文字。