Convex optimization is a subfield of mathematical optimization. Given a real vector space together with a convex, real-valued function
defined on a convex subset of , the problem is to find the point in for which the number is smallest, i.e., the point such that for all .
The convexity of and make the powerful tools of convex analysis applicable: the Hahn–Banach theorem and the theory of subgradients lead to a particularly satisfying and complete theory of necessary and sufficient conditions for optimality, a duality theory comparable in perfection to that for linear programming, and effective computational methods. Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, statistics, and finance. Modern computing power has improved the tractability of convex optimization problems to a level roughly equal to that of linear programming.
Lecture 1
defined on a convex subset of , the problem is to find the point in for which the number is smallest, i.e., the point such that for all .
The convexity of and make the powerful tools of convex analysis applicable: the Hahn–Banach theorem and the theory of subgradients lead to a particularly satisfying and complete theory of necessary and sufficient conditions for optimality, a duality theory comparable in perfection to that for linear programming, and effective computational methods. Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, statistics, and finance. Modern computing power has improved the tractability of convex optimization problems to a level roughly equal to that of linear programming.
Lecture 1
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Lecture 3
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Lecture 6
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd lectures on the localization and cutting-plane methods and then moves into the Analytic center cutting-plane methods.
