非线性规划技术用于均衡状态

English | PDF,EPUB | 2018 (2019 Edition) | 127 Pages | ISBN : 3030002047 | 7.38 MB

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities.

这本书考虑了运筹学中的多种问题，这些问题通过各种数学模型如互补性、变分不等式、多目标优化、不动点问题、非合作博弈和逆优化来表述。此外，本书将所有这些模型归结为一个共同的结构之下，使得它们能够以一种独特的格式进行表述：凯勒-范不等式。随后，它专注于这个统合性均衡格式，并提供对主要理论结果及求解算法的全面概述，同时还包含丰富的应用和数值示例。特别强调了非线性优化技术——例如凸优化、非光滑微积分、投影点算法和下降算法——作为分析和解决凯勒-范不等式的重要工具的价值。

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