Stochastic analysis of an adaptive cubic regularization method under inexact gradient evaluations and dynamic Hessian accuracy

Optimization ◽  
2021 ◽  
pp. 1-35
Author(s):  
Stefania Bellavia ◽  
Gianmarco Gurioli
Keyword(s):  
Regularization Method ◽  
Stochastic Analysis ◽  
Cubic Regularization

scholarly journals Projected Adaptive Cubic Regularization Algorithm with Derivative-Free Filter Technique for Box Constrained Optimization

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lingyun He ◽  
Peng Wang ◽  
Detong Zhu
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Interior Point ◽  
Regularization Method ◽  
Affine Scaling ◽  
Regularization Algorithm ◽  
Filter Technique ◽  
Derivative Free ◽  
Cubic Regularization ◽  
Cubic Model

An adaptive projected affine scaling algorithm of cubic regularization method using a filter technique for solving box constrained optimization without derivatives is put forward in the passage. The affine scaling interior-point cubic model is based on the quadratic probabilistic interpolation approach on the objective function. The new iterations are obtained by the solutions of the projected adaptive cubic regularization algorithm with filter technique. We prove the convergence of the proposed algorithm under some assumptions. Finally, experiments results showed that the presented algorithm is effective in detail.

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