ELEC-E5422 - Convex optimization I D, Lecture, 15.9.2021-15.12.2021
This course space end date is set to 15.12.2021 Search Courses: ELEC-E5422
Topic outline
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Introduction to the course that intends to answer the question what you should expect from the course and what you shouldn't.
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Basics fact of linear algebra and matrix computations used throughout the course of convex optimization.
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subspace, affine set, convex set, convex cone
simple examples and properties
combination and hulls
ellipsoids, polyhedra, norm balls
affine and projective transformations
separating hyperplanes
generalized inequalities
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convex functions, epigraph
simple examples, elementary properties
more examples, more properties
Jensen's inequality
quasiconvex, quasiconcave functions
log-convex and log-concave functions
K-convexity
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abstract form problem
standard form problem
convex optimization problem
standard form with generalized inequalities
mulitcriterion optimization
restriction and relaxation
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• linear programming
• examples and applications
• linear fractional programming
• quadratic optimization problems
• (quadratically constrained) quadratic
programming
• examples and applications
• Semidefinite programming
• applications
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CVX is a modeling system for disciplined convex programming. It will be explained how to use it.
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· terminology
· general descent method
· line search types
· gradient method
· steepest descent method
· Newton's method
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brief history of SUMT & IP methods
· logarithmic barrier function
· central path
· basic SUMT
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Lecture on Sept. 29, 2021
Because the Aalto network was down during the lecture, the beginning of the lecture was lost.
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