Quadratic minimization with norm constraint

Versión (2,84 KB) por Matt J
Minimizes convex or non-convex quadratics subject to (in)equality constraint on norm(x)
411 descargas
Actualizado 24 sep 2017

Ver licencia

This routine minimizes an arbitrary quadratic function subject to a constraint on the l2-norm of the variables. The problem is of a form commonly encountered as a sub-problem in trust region algorithms, but undoubtedly has other applications as well.


[xmin,Jmin] = trustregprob(Q,b,w)
[xmin,Jmin] = trustregprob(Q,b,w,doEquality)

When doEquality=true (the default), the routine solves,

minimize J(x) = x.'*Q*x/2-dot(b,x) such that ||x|| = w

where ||x|| is the l2-norm of x. The variables returned xmin, Jmin are the minimizing x and its objective function value J(x).

When doEquality=false, the routine solves instead subject to ||x|| <= w .

Q is assumed symmetric, but not necessarily positive semi-definite. In other words, the objective function J(x) is potentially non-convex. Since the solution is based on eigen-decomposition, it is appropriate mainly for Q not too large. If multiple solutions exist, only one solution is returned.

Citar como

Matt J (2024). Quadratic minimization with norm constraint (https://www.mathworks.com/matlabcentral/fileexchange/53191-quadratic-minimization-with-norm-constraint), MATLAB Central File Exchange. Recuperado .

Compatibilidad con la versión de MATLAB
Se creó con R2015a
Compatible con cualquier versión
Compatibilidad con las plataformas
Windows macOS Linux

Inspirado por: Least-square with 2-norm constraint

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Versión Publicado Notas de la versión

Improved error checking
Edit title
Edit title

Fixed a bug that affected the special case b=zeros(N,1)

Improved numerical robustness
Fixed a numerical robustness issue

Minor polishes to file description
description edit
Minor edits to help text and description