ECE 580 - Optimization by Vector Space Methods

Semesters Offered

TitleRubricSectionCRNTypeTimesDaysLocationInstructor
Optimiz by Vector Space MethdsECE580D140722LCD0930 - 1050 T R  106B3 Engineering Hall Tamer Basar

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.

Prerequisites

Credit in MATH 415 or MATH 482
Credit in MATH 447

Subject Area

Control Systems

Course Directors

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.

Last updated

2/13/2013