Monday, September 13 2021
10:00am - 12:00pm
PhD Thesis Presentation
Model-Based Derivative-Free Optimization with Unrelaxable Constraints

We develop model-based derivative-free trust-region algorithms for constrained optimization.
Our algorithms are designed for problems in which infeasible points do not provide function values for either the objective or constraints. This restriction poses interesting challenges for ensuring the sample set is well-poised,
meaning the relative positions of sample points ensure the interpolated model functions approximate the true functions well.
To address these challenges, our algorithm constructs feasible ellipsoidal trust regions from which to choose sample points.
The algorithm is first developed for linear constraints and then extended to non-linear constraints.

For non-linear constraints, there is no way to avoid some infeasible function evaluations.
However, the algorithm averts some such evaluation attempts by buffering the feasible region with second-order cones for each nearly-active constraint. Under reasonable assumptions, this buffered region is feasible for sufficiently small trust region radii.
This ensures that the criticality measure for the iterates generated by our algorithm converges to zero.
Speaker:Trever Hallock
Location:see email for zoom link

Download as iCalendar