scholarly journals Some Iterative Numerical Methods for a Kind of System of Mixed Nonlinear Variational Inequalities

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Shuilian Xie ◽  
Hongru Xu ◽  
Huiqing Huang
Keyword(s):  
Numerical Methods ◽  
Variational Inequalities ◽  
Iterative Numerical Methods

scholarly journals A policy iteration algorithm for nonzero-sum stochastic impulse games

2019 ◽  
Vol 65 ◽  
pp. 27-45
Author(s):  
René Aïd ◽  
Francisco Bernal ◽  
Mohamed Mnif ◽  
Diego Zabaljauregui ◽  
Jorge P. Zubelli
Keyword(s):  
Nash Equilibrium ◽  
Numerical Methods ◽  
Variational Inequalities ◽  
Convergence Analysis ◽  
Policy Iteration ◽  
Iteration Algorithm ◽  
Value Functions ◽  
Numerical Tests ◽  
Wide Range ◽  
Policy Iteration Algorithm

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.

scholarly journals Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Björn Haffke ◽  
Riccardo Möller ◽  
Tobias Melz ◽  
Jens Strackeljan
Keyword(s):  
System Identification ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Differential Algebra ◽  
External Validation ◽  
Simulation Models ◽  
Input And Output ◽  
Iterative Numerical Methods

This study deals with the external validation of simulation models using methods from differential algebra. Without any system identification or iterative numerical methods, this approach provides evidence that the equations of a model can represent measured and simulated sets of data. This is very useful to check if a model is, in general, suitable. In addition, the application of this approach to verification of the similarity between the identifiable parameters of two models with different sets of input and output measurements is demonstrated. We present a discussion on how the method can be used to find parameter deviations between any two models. The advantage of this method is its applicability to nonlinear systems as well as its algorithmic nature, which makes it easy to automate.

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