Abstract:

Derivative-freeoptimization (DFO) is essential for problems where derivatives are unavailableor expensive to compute, but its scalability is limited by the high cost ofmodel construction in large dimensions. Subspace techniques address thischallenge by building models and performing optimization in low-dimensionalaffine subspaces.  This talk presents aunified view of subspace modelling and methods for DFO.  We first establish theoretical connectionsbetween full-space and subspace linear and quadratic models and simplexderivatives, showing that they coincide on the underlying subspace and alongorthogonal directions.  We then presentrandom subspace trust-region methods that leverage these models, includingframeworks with provable convergence and complexity guarantees forunconstrained and convex-constrained problems.