Differential stability properties in convex scalar and vector optimization

This paper focuses on formulas for the ε-subdifferential of the optimal value function of scalar and vector convex optimization problems. These formulas can be applied when the set of solutions of the problem is empty. In the scalar case, both unconstrained problems and problems with an inclusion constraint are considered. For the last ones, limiting results are derived, in such a way that no qualification conditions are required. The main mathematical tool is a limiting calculus rule for the ε-subdifferential of the sum of convex and lower semicontinuous functions defined on a (non necessarily reflexive) Banach space. In the vector case, unconstrained problems are studied and exact formulas are derived by linear scalarizations. These results are based on a concept of infimal set, the notion of cone proper set and an ε-subdifferential for convex vector functions due to Taa.

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

We introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

LOAD FORECASTING FOR MONTHS OF THE LUNAR NEW YEAR HOLIDAY USING STANDARDIZED LOAD PROFILE AND SUPPORT REGRESSION VECTOR: CASE STUDY HO CHI MINH CITY

Load forecasting plays an important role in building business strategies, ensuring reliability and safe operation for any electrical system. There are many different methods, including: regression models, time series, neural networks, expert systems, fuzzy logic, machine learning and statistical algorithms used for short-term forecasts. However, the practical requirement is how to minimize the forecast errors to prevent power shortages or wastage in the electricity market and limit risks. For Asian countries (such as Vietnam) that use lunar calendar, one of the most difficult and unpredictable issues is the Lunar New Year (usually in late January or early February). There is a deviation between the solar calendar and the lunar calendar (the load models are not identical). Therefore, it often leads the forecast results of algorithm for this period with large errors. The paper proposes a method of short-term load forecasting by constructing a Standardized Load Profile (SLP) based on the past electrical load data, combining machine learning algorithms Support Regression Vector (SVR) to improve the accuracy of load forecasting algorithms.

LOAD FORECASTING FOR MONTHS OF THE LUNAR NEW YEAR HOLIDAY USING STANDARDIZED LOAD PROFILE AND SUPPORT REGRESSION VECTOR: CASE STUDY HO CHI MINH CITY

Load forecasting plays an important role in building business strategies, ensuring reliability and safe operation for any electrical system. There are many different methods, including: regression models, time series, neural networks, expert systems, fuzzy logic, machine learning and statistical algorithms used for short-term forecasts. However, the practical requirement is how to minimize the forecast errors to prevent power shortages or wastage in the electricity market and limit risks. For Asian countries (such as Vietnam) that use lunar calendar, one of the most difficult and unpredictable issues is the Lunar New Year (usually in late January or early February). There is a deviation between the solar calendar and the lunar calendar (the load models are not identical). Therefore, it often leads the forecast results of algorithm for this period with large errors. The paper proposes a method of short-term load forecasting by constructing a Standardized Load Profile (SLP) based on the past electrical load data, combining machine learning algorithms Support Regression Vector (SVR) to improve the accuracy of load forecasting algorithms.

Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.