L22_10 - Nonlinear Programming (contd) Difficulties of NLP...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Nonlinear Programming (cont’d)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Difficulties of NLP Models Nonlinear Programs: Linear Program:
Background image of page 2
Graphical Analysis of Non-linear programs in two dimensions: An example 22 14 15 () xy −+ Minimize subject to (x - 8) 2 + (y - 9) 2 49 x 2 x 13 x + y 24
Background image of page 3

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

View Full DocumentRight Arrow Icon
Where is the optimal solution? 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 y x Note: the optimal solution is not at a corner point. It is where the isocontour first hits the feasible region.
Background image of page 4
Another example: 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 y x Minimize (x-8) 2 + (y-8) 2 Then the global unconstrained minimum is also feasible. The optimal solution is not on the boundary of the feasible region.
Background image of page 5

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

View Full DocumentRight Arrow Icon
Local vs. Global Optima There may be several locally optimal solutions. x z 1 0 z = f(x) max f(x) s.t. 0 x 1 A B C Def’n : Let x be a feasible solution, then –x is a global max if f(x) f(y) for every feasible y . is a local max if f(x) f(y) for every feasible y sufficiently close to x (i.e., x j - ε≤ y j x j + ε for all j and some small ε ).
Background image of page 6
When is a locally optimal solution also globally optimal? • For minimization problems – The objective function is convex.
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.

Page1 / 28

L22_10 - Nonlinear Programming (contd) Difficulties of NLP...

This preview shows document pages 1 - 8. Sign up to view the full document.

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