{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lec17_10202006

# lec17_10202006 - 10.34 Numerical Methods Applied to...

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

10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #17: Constrained Optimization. Notation “second derivative of f (x ).”: We normally mean f xx Hessian Matrix = 2 2 2 1 2 2 2 1 2 2 1 2 x f x x f x x f x f H V 2 f in BEERS but second derivative can also mean: f xx Laplacian Tr{H } = 2 2 2 2 1 2 x f x f + - scalar V 2 f in Physics Texts V ·( V f ) Constrained Optimization Equality Constraints: min x f (x ) such that g (x ) = 0 May be able to invert this statement as: x N = G ( x 1 , x 2 , …, x N-1 ) Then we can state min as: min f (x 1 , x 2 , …, x N-1 , G ( x 1 , x 2 , …, x N-1 )) Notice the x N is gone. Constrained becomes unconstrained. Solve with previous methods. Other way to do this: Lagrange Multipliers Unconstrained 0 = mn x n x f at the minimum - constrained problems do not work that way! o BOUNDARIES GET IN THE WAY Constrained: min . min . const x n const x n x g x f = λ V f | const. min = λ V g| x const. min Gradient of f equals 0 in directions parallel to constraint but not perpendicular

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.

{[ snackBarMessage ]}

### Page1 / 3

lec17_10202006 - 10.34 Numerical Methods Applied to...

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

View Full Document
Ask a homework question - tutors are online