scholarly journals An iterative method for multiple stopping: convergence and stability

2006 ◽  
Vol 38 (3) ◽  
pp. 729-749 ◽  
Author(s):  
Christian Bender ◽  
John Schoenmakers
Keyword(s):  
Monte Carlo ◽  
Dynamic Programming ◽  
Iterative Method ◽  
Discrete Time ◽  
Iterative Procedure ◽  
Snell Envelope ◽  
Conditional Expectations ◽  
Multiple Stopping ◽  
The Stability ◽  
Monte Carlo Implementation

We present a new iterative procedure for solving the multiple stopping problem in discrete time and discuss the stability of the algorithm. The algorithm produces monotonically increasing approximations of the Snell envelope which coincide with the Snell envelope after finitely many steps. Unlike backward dynamic programming, the algorithm allows us to calculate approximative solutions with only a few nestings of conditional expectations and is, therefore, tailor-made for a plain Monte Carlo implementation.

scholarly journals An iterative method for multiple stopping: convergence and stability

2006 ◽  
Vol 38 (03) ◽  
pp. 729-749 ◽  
Author(s):  
Christian Bender ◽  
John Schoenmakers
Keyword(s):  
Monte Carlo ◽  
Dynamic Programming ◽  
Iterative Method ◽  
Discrete Time ◽  
Iterative Procedure ◽  
Snell Envelope ◽  
Conditional Expectations ◽  
Multiple Stopping ◽  
The Stability ◽  
Monte Carlo Implementation

We present a new iterative procedure for solving the multiple stopping problem in discrete time and discuss the stability of the algorithm. The algorithm produces monotonically increasing approximations of the Snell envelope which coincide with the Snell envelope after finitely many steps. Unlike backward dynamic programming, the algorithm allows us to calculate approximative solutions with only a few nestings of conditional expectations and is, therefore, tailor-made for a plain Monte Carlo implementation.

The method of minimal neighborhood: a new and most effective iterative method for minimum cost trajectory planning in robot manipulators

Robotica ◽  
1995 ◽  
Vol 13 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Ignacy Duleba
Keyword(s):  
Dynamic Programming ◽  
Iterative Method ◽  
Trajectory Planning ◽  
Iterative Procedure ◽  
Optimal Trajectory ◽  
Phase Plane ◽  
Robot Manipulators ◽  
Minimum Cost ◽  
Optimal Trajectory Planning

SummaryIn this paper a method of minimal neighborhood for cost optimal trajectory planning along prescribed paths is introduced. The method exploits the phase-plane approach. In the phase-plane, in an iterative procedure, subareas of search are built, called neighborings, which surround the current-best trajectory. In each iteration, in order to find the next-best trajectory, the dynamic programming (pruned to the subarea) is used. The method of minimal neighborhood makes the neighborings as small as possible and therefore speeds up computations maximally. The tests carried out on a model of the IRb-6 ASEA robot have shown that the method of minimal neighborhood is much faster than dynamic programming applied to the whole phase-plane, while preserving the quality of the resulting trajectory.

scholarly journals On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
The Stability

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Numerical Study of Elasto-Plastic Hydraulic Fracture Propagation in Deep Reservoirs Using a Hybrid EDFM–XFEM Method

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2610
Author(s):  
Wenzheng Liu ◽  
Qingdong Zeng ◽  
Jun Yao ◽  
Ziyou Liu ◽  
Tianliang Li ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Iterative Method ◽  
Hydraulic Fracture ◽  
Iterative Procedure ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Zone Model ◽  
Dilatancy Angle ◽  
Proposed Model ◽  
Hydraulic Fracture Propagation

Rock yielding may well take place during hydraulic fracturing in deep reservoirs. The prevailing models based on the linear elastic fracture mechanics (LEFM) are incapable of describing the evolution process of hydraulic fractures accurately. In this paper, a hydro-elasto-plastic model is proposed to investigate the hydraulic fracture propagation in deep reservoirs. The Drucker–Prager plasticity model, Darcy’s law, cubic law and cohesive zone model are employed to describe the plastic deformation, matrix flow, fracture flow and evolution of hydraulic fractures, respectively. Combining the embedded discrete fracture model (EDFM), extended finite element method (XFEM) and finite volume method, a hybrid numerical scheme is presented to carry out simulations. A dual-layer iterative procedure is developed based on the fixed-stress split method, Picard iterative method and Newton–Raphson iterative method. The iterative procedure is used to deal with the coupling between nonlinear deformation with fracture extension and fluid flow. The proposed model is verified against analytical solutions and other numerical simulation results. A series of numerical cases are performed to investigate the influences of rock plasticity, internal friction angle, dilatancy angle and permeability on hydraulic fracture propagation. Finally, the proposed model is extended to simulate multiple hydraulic fracture propagation. The result shows that plastic deformation can enhance the stress-shadowing effect.

Sign in / Sign up

Export Citation Format

Share Document