Riemannian Multilevel Optimization with Application to Constrained Energy Minimization Problems

Engineering notes

Engineering notes will be added by the Power for Solar editorial team.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。

Original abstract

Multilevel optimization methods are highly effective for discretized energy minimization problems, but their Euclidean formulation does not directly apply to manifold constraints. We introduce a Riemannian extension of multilevel optimization based on a coarse model that is first-order coherent with the fine-level objective and yields descent directions under mild retraction-convexity assumptions. The framework includes metric-compatible vector transfer operators for passing first-order information between levels, covering both intrinsic and extrinsic constructions. We formulate two-level and multilevel algorithms and prove global convergence using a Riemannian Zoutendijk-type argument. Applications to Kohn--Sham density functional theory, Gross--Pitaevskii ground-state computation, and binary continuous cuts demonstrate the method on Stiefel, ellipsoid and Bernoulli manifolds. The experiments show significant reductions in computational time compared with single-level Riemannian optimization.

Links and sources

• Official / arXiv page
• PDF from original source

Comments