Next: About the CONDOR algorithm. Up: An introduction to the Previous: A simple trust-region algorithm.   Contents

# The basic trust-region algorithm (BTR).

Defnition: The trust region is the set of all points such that

 (2.18)

The simple algorithm described in the Section 2.2 can be generalized as follows:
1. Initialization An initial point and an initial trust region radius are given. The constants , , and are also given and satisfy:

 and (2.19)

Compute and set
2. Model definition Choose the norm and define a model in
3. Step computation Compute a step that ''sufficiently reduces the model'' and such that
4. Acceptance of the trial point. Compute and define:

 (2.20)

If , then define ; otherwise define .
5. Trust region radius update. Set

 (2.21)

Increment by 1 and go to step 2.
Under some very weak assumptions, it can be proven that this algorithm is globally convergent to a local optimum [CGT00a]. The proof will be skipped.

Next: About the CONDOR algorithm. Up: An introduction to the Previous: A simple trust-region algorithm.   Contents
Frank Vanden Berghen 2004-04-19