{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Finance Notes_Part_19

# Finance Notes_Part_19 - Fully-linear models For a class of...

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

Fully-linear models For a class of fully-linear models, one must also guarantee that: There exists a model-improvement algorithm , that in a ﬁnite, uniformly bounded (with respect to x and Δ ) number of steps can: certiﬁcate that a given model is fully linear on B ( x ; Δ) , — or (if the above fails), ﬁnd a model that is fully linear on B ( x ; Δ) . Audet and Vicente (SIOPT 2008) Unconstrained optimization 53/109

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

View Full Document
Fully-quadratic models Given a point x and a trust-region radius Δ , a model m ( y ) around x is called fully quadratic if It is twice continuous diﬀerentiable with Lipschitz continuous second derivatives. The following error bounds hold (. ..): k∇ 2 f ( y ) - ∇ 2 m ( y ) k ≤ κ eh Δ y B ( x ; Δ) k∇ f ( y ) - ∇ m ( y ) k ≤ κ eg Δ 2 y B ( x ; Δ) and | f ( y ) - m ( y ) | ≤ κ ef Δ 3 y B ( x ; Δ) . Audet and Vicente (SIOPT 2008) Unconstrained optimization 54/109
TR methods for DFO (basics) Set x k +1 to x k + Δ x k (success)

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 / 5

Finance Notes_Part_19 - Fully-linear models For a class of...

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

View Full Document
Ask a homework question - tutors are online