论文标题
用于大规模优化问题的基于动态子空间的BFGS方法
A Dynamic Subspace Based BFGS Method for Large Scale Optimization Problem
论文作者
论文摘要
大规模的不受约束优化是数值优化中的基本且重要的类别但尚未解决的问题。设计算法的主要挑战是需要一些存储位置或非常便宜的计算，同时保留全球收敛。在这项工作中，我们提出了一种新颖的方法，通过结合动态子空间技术和BFGS更新算法来解决大规模不受限制的优化问题。可以清楚地证明，我们的方法在动态子空间中具有与BFG相比的收敛速率，而与L-BFG相比，内存较少。此外，我们通过构建低维欧几里得空间与自适应子空间的映射来提供收敛分析。我们将混合算法与BFG和L-BFGS方法进行比较。实验结果表明，我们的混合算法提供了几个重要的优势，例如并行计算，收敛效率和鲁棒性。
Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive computations while preserving global convergence. In this work, we propose a novel approach solving large-scale unconstrained optimization problem by combining the dynamic subspace technique and the BFGS update algorithm. It is clearly demonstrated that our approach has the same rate of convergence in the dynamic subspace as the BFGS and less memory than L-BFGS. Further, we give the convergence analysis by constructing the mapping of low-dimensional Euclidean space to the adaptive subspace. We compare our hybrid algorithm with the BFGS and L-BFGS approaches. Experimental results show that our hybrid algorithm offers several significant advantages such as parallel computing, convergence efficiency, and robustness.
