Lecture13-2003 - Lecture XIII Algorithms for Nonlinear...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture XIII Algorithms for Nonlinear Constraints I. General Objective A. The general objective is to maximize or minimize a nonlinear objective function subject to nonlinear constraints. Gill, Murray, and Wright lay out the basic problems: NEP f x st c x i t x i min ( ) ( ) ,.. = = 0 1 and NIP f x st c x i t x i min ( ) ( ) ,... = 0 1 B. These optimization problems are much more difficult than the equality or inequality constraints posed in the preceding sections due to the difficulties involved in maintaining feasiblity. 1. By the formulation of the null-space in the linear equality scenario, it was always possible to guarantee that x k +1 was feasible given that x k was feasible. 2. Similarly, expansion to linear inequality constraints only added caveats to the step length algorithm and checks on whether a constraint could be deleted. 3. However, the solution of nonlinear constraints may be difficult, if not impossible, without the incorporation of a nonlinear objective function. C. I want to discuss three different methodologies for optimization under nonlinear constraints. The first two are the use of penalty and barrier functions. The third procedure is the projected augmented Lagrangian method. II. Penalty Functions
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

Page1 / 3

Lecture13-2003 - Lecture XIII Algorithms for Nonlinear...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online