scholarly journals Monte Carlo Sampling Method for a Class of Box-Constrained Stochastic Variational Inequality Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Pei-Yu Li
Keyword(s):  
Monte Carlo ◽  
Variational Inequality ◽  
Optimization Problem ◽  
Sampling Method ◽  
Monte Carlo Sampling ◽  
Merit Function ◽  
Variational Inequality Problems ◽  
Sufficient Condition ◽  
Existence Of A Solution ◽  
Stochastic Variational Inequality

This paper uses a merit function derived from the Fishcher–Burmeister function and formulates box-constrained stochastic variational inequality problems as an optimization problem that minimizes this merit function. A sufficient condition for the existence of a solution to the optimization problem is suggested. Finally, this paper proposes a Monte Carlo sampling method for solving the problem. Under some moderate conditions, comprehensive convergence analysis is included as well.

SAMPLE AVERAGE APPROXIMATION METHOD FOR SOLVING A DETERMINISTIC FORMULATION FOR BOX CONSTRAINED STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

2012 ◽  
Vol 29 (02) ◽  
pp. 1250014
Author(s):  
MEI-JU LUO ◽  
GUI-HUA LIN
Keyword(s):  
Variational Inequality ◽  
Approximation Method ◽  
Deterministic Model ◽  
Random Parameter ◽  
Sample Average Approximation ◽  
Variational Inequality Problems ◽  
Stochastic Variational Inequality ◽  
Sample Average ◽  
Sample Average Approximation Method ◽  
Average Approximation

In this paper, we discuss the Expected Residual Minimization (ERM) method, which is to minimize the expected residue of some merit function for box constrained stochastic variational inequality problems (BSVIPs). This method provides a deterministic model, which formulates BSVIPs as an optimization problem. We first study the conditions under which the level sets of the ERM problem are bounded. Then, we show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in BSVIPs. Since the integrality involved in the ERM problem is difficult to compute generally, we then employ sample average approximation method to solve it. Finally, we show that the global optimal solutions and generalized KKT points of the approximate problems converge to their counterparts of the ERM problem. On the other hand, as an application, we consider the model of European natural gas market under price uncertainty. Preliminary numerical experiments indicate that the proposed approach is applicable.

scholarly journals An integrated inverse adaptive neural fuzzy system with Monte-Carlo sampling method for operational risk management

2018 ◽  
Vol 98 ◽  
pp. 11-26 ◽  
Author(s):  
Alejandro Peña ◽  
Isis Bonet ◽  
Christian Lochmuller ◽  
Francisco Chiclana ◽  
Mario Góngora
Keyword(s):  
Risk Management ◽  
Monte Carlo ◽  
Fuzzy System ◽  
Sampling Method ◽  
Operational Risk ◽  
Monte Carlo Sampling ◽  
Operational Risk Management ◽  
Neural Fuzzy

Receptor–Ligand Binding Free Energies from a Consecutive Histograms Monte Carlo Sampling Method

2020 ◽  
Vol 16 (10) ◽  
pp. 6645-6655
Author(s):  
Hao Liu ◽  
Jianpeng Deng ◽  
Zhou Luo ◽  
Yawei Lin ◽  
Kenneth M. Merz ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Ligand Binding ◽  
Sampling Method ◽  
Monte Carlo Sampling ◽  
Free Energies ◽  
Receptor Ligand ◽  
Binding Free Energies

Modeling and implementation of spin diode based on two dimensional materials using Monte Carlo sampling method

Circuit World ◽  
2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Swapnali Makdey ◽  
Rajendra Patrikar ◽  
Mohammad Farukh Hashmi
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Density Functional ◽  
Sampling Method ◽  
Spin Current ◽  
Electrical Current ◽  
Monte Carlo Sampling ◽  
Equilibrium Density ◽  
Content Type ◽  
Spin Diode

Purpose A “spin-diode” is the spintronics equivalent of an electrical diode: applying an external magnetic field greater than the limit of spin-diode BT flips the spin-diode between an isolating state and a conducting state [1]. While conventional electrical diodes are two-terminal devices with electrical current between the two terminals modulated by an electrical field, these two-terminal magneto resistive devices can generally be referred to as “spin-diodes” in which a magnetic field modulates the electrical current between the two terminals. Design/methodology/approach Current modulation and rectification are an important subject of electronics as well as spintronics spin diode is two-terminal magnetoresistive devices in which change in resistance in response to an applied magnetic field; this magnetoresistance occurs due to a variety of phenomena and with varying magnitudes and directions. Findings In this paper, an efficient rectifying spin diode is introduced. The resulting spin diode is formed from graphene gallium and indium quantum dots and antimony-doped molybdenum disulfide. Converting an alternating bias voltage to direct current is the main achievement of this model device with an additional profit of rectified spin-current. The non-equilibrium density functional theory with a Monte Carlo sampling method is used to evaluate the flow of electrons and rectification ratio of the system. Originality/value The results indicate that spin diode displaying both spin-current and charge-current rectification should be possible and may find practical application in nanoscale devices that combine logic and memory functions.

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