WAKE FOREST UNIVERSITY
Department of Mathematics & Statistics
Dr. Mostafa Rezapour, Wake Forest University
Thursday, April 29, 2021, 11:00 am via ZOOM
“Adaptive trust-region algorithms for unconstrained optimization problems”
Trust-region methods are a class of numerical methods for optimization. At each
iteration, trust region methods compute a trial step by solving a trust-region subproblem
where a model function is minimized within a trust region. The size of the
trust-region at each step is very critical to the effectiveness of the algorithm,
particularly for large-scale problems.
In this presentation, we discuss two adaptive trust-region algorithms that explore
beyond the trust-region if the boundary of the trust-region prevents the algorithm
from accepting a more beneficial point. It occurs when there is a very good agreement
between the model and the objective function on the trust-region boundary, and we
can find a step outside the trust-region with smaller value of the model while at
which the agreement between the model and the objective function remains good.
We show that the proposed algorithms are convergent. Moreover, the numerical
experiments show that the proposed algorithms are more efficient than the traditional
trust-region algorithm for a large majority of problems in the CUTEst problem set.