On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization
Behzad Azmi, Karl Kunisch
Abstract
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.
Topics & Concepts
MathematicsConvergence (economics)Partial differential equationDifferentiable functionApplied mathematicsPartial derivativeClass (philosophy)Mathematical analysisMathematical optimizationComputer scienceEconomic growthArtificial intelligenceEconomicsAdvanced Optimization Algorithms ResearchIterative Methods for Nonlinear EquationsMatrix Theory and Algorithms