Algebraic Techniques and Semidefinite Optimization
MIT OpenCourseWare offers this graduate-level course on algebraic and computational methods for optimization problems built from polynomial equations and inequalities. The syllabus develops semidefinite optimization alongside algebraic geometry approaches, covering both complex and real polynomial systems, convexity-based methods, and complexity results for solving them efficiently. Examples are drawn from engineering, with particular attention to systems and control applications. Materials include lecture notes and problem sets from the MIT course, aimed at students already comfortable with linear algebra and optimization theory who want to see how algebraic techniques and semidefinite programming reinforce each other. The course is free to access through MIT OpenCourseWare, with no certificate offered.