تقرير
Fast Convergence to Second-Order Stationary Point through Random Subspace Optimization
| العنوان: | Fast Convergence to Second-Order Stationary Point through Random Subspace Optimization |
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| المؤلفون: | Higuchi, Rei, Poirion, Pierre-Louis, Takeda, Akiko |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, 90C06, 90C26, 90C30 |
| الوصف: | We propose the Random Subspace Homogenized Trust Region (RSHTR) method, which efficiently solves high-dimensional non-convex optimization problems by identifying descent directions within randomly selected subspaces. RSHTR provides the strongest theoretical guarantees among random subspace algorithms for non-convex optimization, achieving an $\varepsilon$-approximate first-order stationary point in $O(\varepsilon^{-3/2})$ iterations and converging locally at a linear rate. Furthermore, under rank-deficient conditions, RSHTR satisfies $\varepsilon$-approximate second-order necessary condition in $O(\varepsilon^{-3/2})$ iterations and exhibits a local quadratic convergence. Comment: 39 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.14337 |
| رقم الأكسشن: | edsarx.2406.14337 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |