scholarly journals On the Convergence Analysis of Cubic Regularized Symmetric Rank-1 Quasi-Newton Method and the Incremental Version in the Application of Large-Scale Problems

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 114042-114059
Author(s):  
Huiming Chen ◽  
Wong-Hing Lam ◽  
Shing-Chow Chan
Keyword(s):  
Convergence Analysis ◽  
Newton Method ◽  
Large Scale ◽  
Large Scale Problems ◽  
Quasi Newton

scholarly journals A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization With Applications

2020 ◽  
Vol 31 (11) ◽  
pp. 4776-4790 ◽  
Author(s):  
Huiming Chen ◽  
Ho-Chun Wu ◽  
Shing-Chow Chan ◽  
Wong-Hing Lam
Keyword(s):  
Newton Method ◽  
Nonconvex Optimization ◽  
Large Scale ◽  
Quasi Newton

scholarly journals A Stochastic Quasi-Newton Method for Large-Scale Optimization

2016 ◽  
Vol 26 (2) ◽  
pp. 1008-1031 ◽  
Author(s):  
R. H. Byrd ◽  
S. L. Hansen ◽  
Jorge Nocedal ◽  
Y. Singer
Keyword(s):  
Newton Method ◽  
Large Scale ◽  
Large Scale Optimization ◽  
Scale Optimization ◽  
Quasi Newton

scholarly journals A matrix-free quasi-Newton method for solving large-scale nonlinear systems

2011 ◽  
Vol 62 (5) ◽  
pp. 2354-2363 ◽  
Author(s):  
Wah June Leong ◽  
Malik Abu Hassan ◽  
Muhammad Waziri Yusuf
Keyword(s):  
Nonlinear Systems ◽  
Newton Method ◽  
Large Scale ◽  
Quasi Newton ◽  
Matrix Free

AUTOMATED OPTION PRICING: NUMERICAL METHODS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350042 ◽  
Author(s):  
PIERRE HENRY-LABORDÈRE
Keyword(s):  
Large Scale ◽  
Prior Probability ◽  
Interior Point Algorithm ◽  
Option Prices ◽  
Large Scale Problems ◽  
Convex Problem ◽  
Primal Dual ◽  
Model Independent ◽  
Quasi Newton ◽  
Infinite Linear

In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing problem. As these super-replication prices can be large and the densities ℚ which achieve the upper bounds quite singular, we restrict ℚ to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral weighted Monte Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.

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