11qnewton

11qnewton - EE236C (Spring 2008-09) 11. Quasi-Newton...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: EE236C (Spring 2008-09) 11. Quasi-Newton methods variable metric methods quasi-Newton methods BFGS update limited-memory quasi-Newton methods 111 Newton method for unconstrained minimization minimize f ( x ) f convex, twice continously differentiable Newton method x + = x t 2 f ( x ) 1 f ( x ) advantages: fast convergence, affine invariance disadvantages: requires second derivatives, solution of linear equation can be too expensive for large scale applications Quasi-Newton methods 112 Variable metric methods x + = x tH 1 f ( x ) H is approximation of the Hessian at x , chosen to: avoid calculation of second derivatives simplify computation of search direction variable metric interpretation (EE236B, lecture 10, page 11) x = H 1 f ( x ) is steepest descent direction at x for quadratic norm bardbl z bardbl H = ( z T Hz ) 1 / 2 Quasi-Newton methods 113 Quasi-Newton methods given starting point x (0) dom f , H for k = 1 , 2 , . . . , until a stopping criterion is satisfied 1. compute quasi-Newton direction x = H 1 k 1 f ( x ( k 1) ) 2. determine step size t ( e.g. , by backtracking line search) 3. compute x ( k ) = x ( k 1) + t x 4. compute H k different methods use different rules for updating H in step 4 can also propagate H 1 k to simplify calculation of x Quasi-Newton methods 114 Broyden-Fletcher-Goldfarb-Shanno (BFGS) update H k = H k 1 + yy T...
View Full Document

This note was uploaded on 01/25/2010 for the course EE 236 taught by Professor Staff during the Spring '08 term at UCLA.

Page1 / 7

11qnewton - EE236C (Spring 2008-09) 11. Quasi-Newton...

This preview shows document pages 1 - 4. Sign up to view the full document.

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