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# 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