On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization

Abstract

Aiming at optimization problems governed by partial differential equations (PDEs), local R-linear convergence of the Barzilai–Borwein (BB) method for a class of twice continuously Fréchet-differentiable functions is proven. Relying on this result, the mesh-independent principle for the BB-method is investigated. The applicability of the theoretical results is demonstrated for two different types of PDE-constrained optimization problems. Numerical experiments are given, which illustrate the theoretical results.

Barzilai–Borwein method, R-linear rate of convergence, mesh independence, PDE-constrained optimization