Bounded perturbation resilience of extragradient-type methods and their applications

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorizion can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converges at the rate of $O(1/t)$. Numerical illustrations are given to demonstrate the performances of the algorithms.Comment: Accepted for publication in The Journal of Inequalities and Applications. arXiv admin note: text overlap with arXiv:1711.01936 and text overlap with arXiv:1507.07302 by other author

Are there interactive effects of physiological and radiative forcing produced by increased CO2 concentration on changes of land hydrological cycle?

AbstractThree coupled climate–carbon cycle models including CESM (Community Earth System Model), CanEsm (the Canadian Centre for Climate Modelling and Analysis Earth System Model) and BCC (Beijing Climate Center Climate System Model) were used to estimate whether changes in land hydrological cycle responded to the interactive effects of CO2-physiological forcing and CO2-radiative forcing. No signs could be indicated that the interactive effects of CO2-physiological forcing and CO2-radiative forcing on the hydrological variables (e.g. precipitation, evapotranspiration and runoff) were detected at global and regional scales. For each model, increases in precipitation, evapotranspiration and runoff (e.g. 0.37, 0.18 and 0.25mm/year2) were simulated in response to CO2-radiative forcing (experiment M3). Decreases in precipitation and evapotranspiration (about −0.02 and −0.09mm/year2) were captured if the CO2 physiological effect was only accounted for (experiment M2). In this experiment, a reverse sign in runoff (the increase of 0.08mm/year2) in contrast to M3 is presented. All models simulated the same signs across Eastern Asia in response to the CO2 physiological forcing and radiative forcing: increases in precipitation and evapotranspiration only considering greenhouse effect; reductions in precipitation and evapotranspiration in response to CO2-physiological effect; and enhanced trends in runoff from all experiments. However, there was still a large uncertainty on the magnitude of the effect of transpiration on runoff (decreased transpiration accounting for 8% to 250% of the increased runoff) from the three models. Two models (CanEsm and BCC) attributed most of the increase in runoff to the decrease in transpiration if the CO2-physiological effect was only accounted for, whereas CESM exhibited that the decrease in transpiration could not totally explain the increase in runoff. The attribution of the CO2-physiological forcing to changes in stomatal conductance versus changes in vegetation structure (e.g. increased Leaf Area Index) is an issue to discuss, and among the three models, no agreement appeared

Is there Two-Way Information Transmission between Stock Markets and Stock Discussion Boards?

This research investigates information transmissions between stock returns and abnormal posting volumes using a total of 1,031,206 messages posted on Chinese stock message boards. Based on a multivariable GARCH (1, 1) model and causality in variance test, the study shows that there are significant two-way volatility spillovers effects: a positive volatility spillover effect from stock returns to abnormal posting volume, and a negative volatility spillover effect from abnormal posting volume to stock returns. The information exchange and communication on stock message boards have a certain role to stabilize financial markets and to improve the investment rationale

8-Chloro-4-cyclo­hexyl-2H-1,4-benzoxazin-3(4H)-one

In the crystal structure of title compound, C14H16ClNO2, the cyclo­hexyl ring is in a chair conformation. The molecules are connected into centrosymmetric dimers via weak C—H⋯O hydrogen bonds