ECE 580

ECE 580 - Optimization by Vector Space Methods

Fall 2024

Title	Rubric	Section	CRN	Type	Hours	Times	Days	Location	Instructor
Optimiz by Vector Space Methds	ECE580	N	33577	LCD	4	0930 - 1050	T R	2017 Electrical & Computer Eng Bldg	Maxim Raginsky

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Web Page

https://maxim.ece.illinois.edu/teaching/fall24/

Official Description

Normed, Banach, and Hilbert spaces; applications of the projection theorem and the Hahn-Banach Theorem to problems of minimum norm, least squares estimation, mathematical programming, and optimal control; the Kuhn-Tucker Theorem and Pontryagin's maximum principle; iterative methods. Course Information: Prerequisite: MATH 415 or MATH 482; MATH 447.

Subject Area

General Sciences

Course Director

Tamer Basar

Description

Introduction to normed, Banach, and Hilbert spaces; applications of the projection theorem and the Hahn-Banach Theorem to problems of minimum norm, least squares estimation, mathematical programming, and optimal control; the Kuhn-Tucker Theorem and Pontryagin's maximum principle; and introduction to iterative methods.

Notes

Same as MATH 587.

Topics

Normed vector spaces
Iterative methods, fixed-point theorems
Hilbert spaces - the projection theorem
Hahn-Banach theorem: minimum norm problems
Optimization problems in Hilbert and Banach spaces
Local and global theory of constrained optimization: nonlinear programming and the Kuhn-Tucker theorem; optimal control and Pontryagin's minimum principle

Detailed Description and Outline

Topics:

Normed vector spaces
Iterative methods, fixed-point theorems
Hilbert spaces - the projection theorem
Hahn-Banach theorem: minimum norm problems
Optimization problems in Hilbert and Banach spaces
Local and global theory of constrained optimization: nonlinear programming and the Kuhn-Tucker theorem; optimal control and Pontryagin's minimum principle