A quasi-Newton interior-point method for optimization in Hilbert spaces
Cosmin G. Petra · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2021
We present a quasi-Newton interior-point method appropriate for optimization problems with pointwise inequality constraints in generic Hilbert function spaces.Among others, our methodology applies to optimization problems constrained by partial differential equations (PDEs) that are posed in a reduced-space formulation and have bounds or inequality constraints on the optimized parameter function.The mathematically sound formalization of an infinite-dimensional quasi-Newton interior-point algorithm using secant updates presented in the paper is complemented with a judicious derivation of a mesh-independent discretized interior-point method that can work generically with various discretization schemes for the underlying Hilbert space.A previously introduced parallelization approach for limited-memory quasi-Newton methods is herein formulated in an infinite-dimensional space and used to solve an extreme-scale structural topology optimization with 880 million design variables using 9 216 cores of the Quartz cluster at Lawrence Livermore National Laboratory (LLNL).We also propose a streamlined parallel optimization solver interface that allows using a wide range of solvers for PDEs or other differential equations.Finally, we report the strengths and the limitations of the proposed methodology on several classes of PDE-constrained problems.