high-order proximal point algorithm for the monotone variational inequality problem and its application

The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction method of multipliers (ADMM). This paper generalizes the PPA to the $p$th-order ($p\geq 1$) and proves its convergence rate $O \left(1/k^{p/2}\right)$ . Additionally, the $p$th-order ALM is proposed based on the $p$th-order PPA. Some numerical experiments are presented to demonstrate the performance of the $p$th-order ALM

A linearly convergent method for solving high-order proximal operator

Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In this paper, we present a linearly convergent method to solve the high-order proximal operator based on the classical proximal operator. In addition, some experiments are performed to demonstrate the performance of the proposed method

Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule

A novel three-dimensional (3D) fractional plastic flow rule that is not limited by the coordinate basis of the differentiable function is proposed based on the fractional derivative and the coordinate transformation. By introducing the 3D fractional plastic flow rule into the characteristic stress space, a 3D fractional elastoplastic model for soil is established for the first time. Only five material parameters with clear physical significance are required in the proposed model. The capability of the model in capturing the strength and deformation behaviour of soils under true 3D stress conditions is verified by comparing model predictions with test results

The study of a seasonal solar cchp system based on evacuated flat-plate collectors and organic rankine cycle

The demands of cooling, heating and electricity in residential buildings are varied with seasons. This article presented a seasonal solar combined cooling heating and power (CCHP) system based on evacuated flat-plate collectors and organic Rankine cycle. The heat collected by evacuated flat-plate collectors is used to drive the organic Rankine cycle unit in spring, autumn and winter, and drive the double-effect lithium bromide absorption chiller in summer. The organic Rankine cycle condensation heat is used to yield hot water in spring and autumn, whereas supply heating in winter. The system thermodynamic performance was analyzed. The results show that the system thermal efficiency in spring, autumn and winter, ηsys, I, increases as organic Rankine cycle evaporation temperature, T6, and evacuated flat-plate collectors outlet temperature, T2, decrease. The maximum ηsys, I of 67.0% is achieved when T6 = 80 °C and T2 =100 °C. In summer, the system thermal efficiency, ηsys, II, increases first and then decreases with the increment of T2. The maximum ηsys, II of 69.9% is obtained at T2 =136 °C. The system output performance in Beijing and Lanzhou is better than that in Hefei. The average output power, heating capacity, hot water and cooling capacity are 50-72 kWh per day, 989-1514 kWh per day, 49-57 ton per day and 1812-2311 kWh per day, respectively. The system exergy efficiency increases from 17.8-40.8% after integrating the organic Rankine cycle unit

The impact of internet use on rural household energy transition: moderating effect based on social interaction

Introduction: Household energy transition is the key to changing and upgrading China’s energy consumption pattern. Directly using traditional biomass fuels is not only one of the reasons why the opportunity between urban and rural areas is inequality but also a critical symbol of the inequality of energy consumption within rural areas.Method: This study investigates the association between two information acquisition mechanisms, namely, Internet use and social interaction, and rural household energy transition, using CGSS 2015. After converting the consumption of each fuel to standard coal, according to the energy ladder theory, this study classifies the main types of household energy into three categories: primitive fuels, transition fuels, and advanced fuels. Then this study uses the ordered probit model to empirically analyze 1023 rural household samples in China.Results: The results show that, compared to rural households that never use the Internet, an increase in the frequency of Internet use significantly enhances the probability of rural households using advanced fuels, while decreasing the probability of using primitive and transition fuels simultaneously. However, the effect direction of social interaction works is the opposite of Internet use completely. The intrinsic mechanism result shows that although social interaction reduces the strength of the role of Internet use in rural household energy transition, it has not yet completely offset the positive effect of Internet use on the rural household energy transition.Discussion: The results of this study provide references for removing the blocking barriers to contact and use of the Internet by rural residents, improving the perceived quality of obtained information through social interaction, and solidly promoting rural energy transition and sustainable development of resources and the environment

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms. To exploit the potential of generalized algorithms using t-scalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to "deeper-order" t-scalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.Comment: 20 pages, several typos corrected, one appendix adde