تقرير
Improved Convergence Bounds For Operator Splitting Algorithms With Rare Extreme Errors
العنوان: | Improved Convergence Bounds For Operator Splitting Algorithms With Rare Extreme Errors |
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المؤلفون: | Hamadouche, Anis, Wallace, Andrew M., Mota, Joao F. C. |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Signal Processing, 49M37, 65K05, 90C25 |
الوصف: | In this paper, we improve upon our previous work[24,22] and establish convergence bounds on the objective function values of approximate proximal-gradient descent (AxPGD), approximate accelerated proximal-gradient descent (AxAPGD) and approximate proximal ADMM (AxWLM-ADMM) schemes. We consider approximation errors that manifest rare extreme events and we propagate their effects through iterations. We establish probabilistic asymptotic and non-asymptotic convergence bounds as functions of the range (upper/lower bounds) and variance of approximation errors. We use the derived bound to assess AxPGD in a sparse model predictive control of a spacecraft system and compare its accuracy with previously derived bounds. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2306.16964 |
رقم الأكسشن: | edsarx.2306.16964 |
قاعدة البيانات: | arXiv |
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