Trust region algorithms are strongly convergent, typically restricting the step to lie within a spherical trust region.
Structured trust region algorithms attempt greater efficiency by allowing differing trust region radii in different partially separable subspaces. However, the unpredictable shape of this trust region takes away some convergence strength for naive implementations. Restrictions on the step have been proposed in earlier work to correct this.
We propose a trust region radius update mechanism that depends on the change in gradient direction between iterations and thus avoids restrictions on the step. To simplify the analysis, we limit ourselves to the unconstrained problem, and show first and second order global convergence. We also make the simplification that the range spaces are defined by canonical basis vectors.
By: Johara Shahabuddin
Published in: RI02002 in 2002
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