Basics of Convex Optimization with Application

Course title: Basics of Convex Optimization with Application

Code: 3ФЕИТ08З013

Number of credits (ECTS): 6

Weekly number of classes: 3+2+0+0

Prerequisite for enrollment of the subject: None

Course Goals (acquired competencies): Familiarization with the basic theory of convex optimization. Recognizing and solving convex optimization problems for electrical engineering.

Total available number of classes: 180

Course Syllabus: The notion of mathematical optimization. Importance of convex optimization in electrical engineering and ICT (examples). Convexity versus nonconvexity. Optimization without restriction. Illustrative examples of electrical engineering. Convex sets. Convex functions. Convex optimization problems. Equivalent problems. Criteria for optimum. Duality. Lagrange Function. Conditions for optimum. The Karush-Kuhn-Tucker theorem. Convex optimization with least squares. Linear programming. Application in optimization of signal strength. Application of numerical algorithms in optimization problems. Internal point method. Using CVX solver in Matlab. Convex relaxation. Application in optimum design of systems and networks. Optimization problems in telecommunication engineering. Application in optimization of ICT-based systems.

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