Questions tagged [trust-regions]

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Deriving the Cauchy point of the horizontal subproblem for large-scale trust-region SQP

I am having difficulty deriving the Cauchy point of the horizontal subproblem $$ \overline{g}_k^T Z_k u + \frac{1}{2} u^T Z_k^T W_k Z_k u \;\;\;\;\mbox{subject to}\;\; \mid \mid Z_k u \mid\mid_2 $$ ...
Olumide's user avatar
  • 255
3 votes
1 answer

Good languages/packages for interior point optimization with non-linear constraints?

I'm currently using Python's scipy.optimize package to perform parameter estimation for a system of 10 ODEs. I have some observed data, and I'm trying to find the set of parameters which makes the ODE ...
Leonidas's user avatar
  • 153
1 vote
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Solve scalar quadratic equation

I am implementing a Trust-Region method using Dogleg for the search direction defined as $\tau p^U$ for $0 \leq \tau \leq 1$ and $p^U + (\tau -1)(p^B-p^U)$ if $1 \leq \tau \leq 2$. To compute $\tau$ ...
wrong_path's user avatar
6 votes
1 answer

Global convergence in trust region algorithm

I was reading about TR methods and there are some terms, which are confusing for me. It says, method is globaly convergent. What does it really mean? Converges to global minima, or converges for ...
bla_bla_bla's user avatar
5 votes
1 answer

scaling and preconditioning for trust region Newton methods

Geometrically, scaling and preconditioning seem to address similar challenges in optimization. However, these two concepts are implemented very differently. Take trust region Newton method, as an ...
Hari's user avatar
  • 666
7 votes
1 answer

Python trust region optimization code that allows ellipsoid-shaped trust regions

Are there any high quality trust region optimization implementations that allow nonspherical ellipsoid trust regions, and are written in Python, or are easy to call from python? By nonspherical ...
Nick Alger's user avatar
  • 3,063