Homework 04

# Homework 04 - IEOR E4007 G Iyengar March 30th 2009 Homework...

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

IEOR E4007 G. Iyengar March 30th, 2009 Homework # 4 Due: April 12th, 2009 1. Problem on unconstrained optimization For each of the following optimization problems either verify that the given x is a stationary point or ﬁnd a direction d that locally improves at x . (a) max 10 x 2 1 + 12 ln( x 2 ), x = (1 , 2) (b) max x 1 x 2 - 10 x 1 + 4 x 2 , x = ( - 4 , 10) 2. Local optimality For each of the following functions f , classify the speciﬁed x as a deﬁnitely a local maximum, possibly local maximum, deﬁnitely local minimum, possibly local minimum or none of the above. (a) f ( x ) = - x 2 1 - 6 x 1 x 2 - 9 x 2 2 , x = ( - 3 , 1) (b) f ( x ) = 12 x 2 - x 2 1 + 3 x 1 x 2 - 3 x 2 2 , x = (12 , 8) (c) f ( x ) = 6 x 1 + ln( x 1 ) + x 2 2 , x = (1 , 2) (d) f ( x ) = 4 x 2 1 + 3 /x 2 - 8 x 1 + 3 x 2 , x = (1 , 1) 3. Problem on recognizing convex functions/sets Determine whether each of the following is a convex program (a) min { x 1 + x 2 : x 1 x 2 9 , | x 1 | ≤ 5 , | x 2 | ≤ 5 } (b) max { 62 x 1

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/02/2010 for the course IEOR IEOR E4007 taught by Professor Optimizationmodelsandmethods during the Summer '09 term at Columbia.

### Page1 / 3

Homework 04 - IEOR E4007 G Iyengar March 30th 2009 Homework...

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

View Full Document
Ask a homework question - tutors are online