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Algebraic Techniques and Semidefinite Optimization OpenCourseWare: MIT's Free Graduate Level Course on Algebraic Techniques

Published Jan 15, 2009

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The Massachusetts Institute of Technology (MIT) has made available 'Algebraic Techniques and Semidefinite Optimization' as free OpenCourseWare. It was originally taught to graduate students in the Department of Electrical Engineering and Computer Science. The course deals with mathematical sets and their properties, both computational and mathematical. The sets studied can be characterized by inequalities and polynomial equations.

Algebraic Techniques and Semidefinite Optimization: Course Specifics

Degree Level Free Audio Video Downloads
Graduate Yes No No Yes

Lectures/Notes Study Materials Tests/Quizzes
Yes Yes No

Algebraic Techniques and Semidefinite Optimization: Course Description

Semidefinite optimization (also known as semidefinite programming) specifically deals with choosing a symmetric matrix (which must be positive semidefinite) to optimize a linear function subject to linear constraints. This course expands on both prior algebra and optimization knowledge in a real-world context with topics, such as binary optimization, positive semidefinite matrices, positive polynomials, quantifier elimination, zero-dimensional ideals and Newton polytopes among other topics. Essentially, this course is an applied mathematics course using many examples from different engineering areas, but having a focus on systems and control applications. Besides having a firm grasp of general mathematical concepts, a background in basic probability, linear algebra and convex analysis or linear optimization is necessary. Professor Pablo Parrilo taught the original course to grads in the Department of Electrical Engineering and Computer Science using lectures.

'Algebraic Techniques and Semidefinite Optimization' OpenCourseWare contains lecture notes, assignments, reading list and semidefinite programming software code. If this course strikes a note with you and you would like to investigate further, then visit the computational and algebraic techniques and inequalities and polynomial equations course page.

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