非线性组合优化暑期学校暨学术前沿研讨会

项目名称： 非线性组合优化暑期学校暨学术前沿研讨会

项目编号： No.11726003

项目类型： 专项基金项目

立项/批准年度： 2017

项目学科： 数理科学和化学

项目作者： 徐大川

作者单位： 北京工业大学

项目金额： 60万元

中文摘要： 组合优化是属于运筹学、管理科学和计算机科学的一门交叉学科，它在当今快速发展的信息时代愈发凸显重要；而大量具有离散结构的实际优化问题使得非线性组合优化倍受关注，使其成为组合优化的一个新兴研究领域。本次暑期学校围绕非线性组合优化的核心内容，将开设《非线性组合化》、《次模优化理论与算法》及《离散凸分析》三门课程；其中《非线性组合优化》将统筹介绍针对非线性组合优化的理论和算法设计分析；《次模优化理论与算法》从具有离散优化背景的次模优化问题出发，介绍其中基本理论、算法和应用；《离散凸分析》则对凸集合和凸函数做推广，介绍相应的分离定理和对偶理论，以及局部极小和全局极小的最优准则等。在暑期学校的最后阶段，我们将组织为期一天半的学术前沿报告会，届时我们将邀请十多位非线性组合优化及相关领域的专家学者参会，报告他们最新的研究成果，为参加暑期学校的研究生和青年教师提供夯实基础、开拓视野、提高水平的学习平台。

中文关键词： 非线性组合优化；次模优化；离散凸分析；暑期学校

英文摘要： In nowadays of rapid development of information, as the operations research, management science and theoretical computer science interdisciplinary, combinatorial optimization is much more important. Additionally a large number of optimization problems with discrete structures make the nonlinear combinatorial optimization more attractable and become a new research direction of combinatorial optimization. Surrounding the core contents in the field of nonlinear combinatorial optimization, this summer school sets up three courses: “Nolinear Combinatorial Optimization”, “The Theories and Algorithms of Submoluar Optimization” and “Discrete Convex Analysis”. Course “Nolinear Combinatorial Optimization” overall introduces the theories and algorithms of nolinear combinatorial optimization; “The Theories and Algorithms of Submoluar Optimization” introduces the basic theories, algorithms and applications for the submodular optimization problems with actual discrete optimization background; and “Discrete Convex Analysis” generalizes the convex sets and convex functions, and introduces corresponding separation theorem and duality theory, the optimal criterions of local and global minimum, etc. In the final section of summer school, we will organize an academic research seminar by inviting a dozen leading experts in relevant areas. Then these experts will propose their latest research results. This summer school just is to build up the solid foundation, broaden the horizons and improve the level of learning platform for the graduate students and young scientists in the nonlinear combinatorial optimization and related fields.

英文关键词： Nonlinear Combinatorial Optimizartion;Submodular Optimization ;Discrete Convex Analysis;Summer School