# ECE 580

## ECE 580 - Optimization by Vector Space Methods

### Fall 2021

TitleRubricSectionCRNTypeHoursTimesDaysLocationInstructor
Optimiz by Vector Space MethdsECE580N33577LCD40930 - 1050 T R  3015 Electrical & Computer Eng Bldg Maxim Raginsky

### 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

### 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

Same as MATH 587.

### Texts

D.G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, 1969.

2/13/2013