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代数方法和半正定优化

6.972 Algebraic Techniques and Semidefinite Optimization
课程网址: http://ocw.mit.edu/courses/electrical-engineering-and-computer-sc...  
主讲教师: Prof. Pablo Parrilo
开课单位: 麻省理工学院
开课时间: 2006-01-01
课程语种: 英语
中文简介:
本研究为导向的课程将侧重于涉及多项式方程和不等式的优化问题的代数和计算技术, 特别强调与半定优化的联系。本课程将以并行的方式开发多项式系统的几种代数和数值方法, 以期同时将这两个元素结合起来的方法。我们将研究复杂和真实的案例, 开发具有普遍适用性的技术, 并强调基于凸的思想、复杂性结果和有效的实现。虽然我们将使用来自多个工程领域的示例, 但将特别强调系统和控制应用中产生的示例。
课程简介: This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.
关 键 词: 计算技术; 优化问题; 多项式方程; 半正定优化
课程来源: 麻省理工大学公开课
最后编审: 2024-05-23:chenjy
阅读次数: 28