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Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques
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We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author under the supervision of Ya-xiang Yuan. At each iteration, the framework defines a (low-dimensional) subspace based on an approximate gradient, and then solves a subproblem in this subspace to generate a new iterate. We sketch the global convergence and worst-case complexity analysis of the framework, elaborate on its implementation, and present some numerical results on solving problems with dimensions as high as 10^4 using only inaccurate function values.
Forward citations
Cited by 2 Pith papers
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Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy
The paper proposes truncated, model-gradient-generated subspaces for large-scale optimization and gives conditional decrease and convergence theorems, but the stated guarantees are not fully proven.
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A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems
UPOQA exploits partial separability by building individual quadratic models with per-element trust regions and an approximate 'Steinmetz projection', cutting function evaluations versus baselines in numerical tests.
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