{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

TrustRegion - Stanford University Trust-Region Methods D...

Info icon This preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
Stanford University PE284 Trust-Region Methods D. Echeverría Ciaurri Optimization PE284 Stanford University
Image of page 1

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 2 Outline Basic Idea The Cauchy Point Algorithms Convergence Constrained Problems Summary
Image of page 2
Stanford University Trust-Region Methods Nov 3 2008 PE284 3 Trust-Region Methods Optimization with safeguards Dual to line search Related to Levenberg ‘Trust Region’ coined by Dennis Applied in great number of fields Included in MATLAB’s fmincon
Image of page 3

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 4 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 4
Stanford University Trust-Region Methods Nov 3 2008 PE284 5 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 5

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 6 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 6
Stanford University Trust-Region Methods Nov 3 2008 PE284 7 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 7

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 8 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 8
Stanford University Trust-Region Methods Nov 3 2008 PE284 9 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 9

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 10 Main Idea (figures from http://www.applied-mathematics.net)
Image of page 10
Stanford University Trust-Region Methods Nov 3 2008 PE284 11 Trust-Region Step Unconstrained minimization of f(x) with B k symmetric uniformly bounded Solve approximately where k >0 is the trust-region radius ( 29 k 2 k T 2 1 T k k k R p || p || s.t. p B p p f f p m min n + + = ( 29 ( 29 ( 29 k 2 k k k k k k x f B , x f f , x f f , x = =
Image of page 11

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 12 Trust-Region Step Step p k acceptance + TR control by ( 29 ( 29 ( 29 ( 29 k k k k k k k p m 0 m p x f x f - + - = ρ actual predicted
Image of page 12
Stanford University Trust-Region Methods Nov 3 2008 PE284 13 Trust-Region Step Step p k acceptance + TR control by If ρ k ~ 1 or larger: accept + expand TR If ρ k medium: accept If ρ k small: reject + shrink TR ( 29 ( 29 ( 29 ( 29 k k k k k k k p m 0 m p x f x f - + - = ρ actual predicted
Image of page 13

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 14 Basic Algorithm Given MAX >0, 0 and 0 ≤ η < η 1 < η 2 and γ 1 < 1 < γ 2 : for i = 0,1,2,… Obtain p k by approx. solving min m k (p) in TR Evaluate ρ k if ρ k < η 1 k+1 = γ 1 || p k || else if ρ k > η 2 and k+1 = || p k || k+1 = min( γ 2 k , , MAX ) else k+1 = k if ρ k > η x k+1 = x k + p k else x k+1 = x k end(for);
Image of page 14
Stanford University Trust-Region Methods Nov 3 2008 PE284 15 Outline Basic Idea The Cauchy Point Algorithms Convergence Constrained Problems Summary
Image of page 15

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

View Full Document Right Arrow Icon
Stanford University Trust-Region Methods Nov 3 2008 PE284 16 The Cauchy Point Crucial for global convergence Defines the approximation level Minimizes m k (p) along s.t.
Image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern