Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization

In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

A Proximal Algorithm with Convergence Guarantee for a Nonconvex Minimization Problem Based on Reproducing Kernel Hilbert Space

The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with ℓ0-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKHS can be represented by the linear combination of reproducing kernels and their coefficients. Thus, we turn to estimate the related coefficients in the nonconvex minimization problem. An efficient algorithm is designed to solve the given nonconvex problem by the mathematical program with equilibrium constraints (MPEC) and proximal-based strategy. We theoretically prove that the sequences generated by the designed algorithm converge to the nonconvex problem’s local optimal solutions. Numerical experiment also demonstrates the effectiveness of the proposed method.

Influence Metal Berylliumof the Optical FiberCoreon plasmonic Properties

The paper include, the properties of the plasmonic optical fiber in which the core is beryllium metal were studied, were we studied the effect of this metal on the plasmonic fiber, and a mathematical program was used which is COMSOL MULTIPHYSICS, which depends on the finite element method (FEM) to deduce the first three modes and the effective refractive index, neff accompanying each wavelength. It was observed that when order the mode is increased, the lobes will increase, where the mode, LP 01 is one spot and the mode, LP11 are two spots and the mode, LP21 are four spots. An increase in the power indicator is increase red and yellow, and this applies to all modes. That is, by controlling the radius of the fiber core and the wavelength, it is possible to equilibrium the power ratio that propagates forward and backward. The neff , attenuation coefficient and propagation constant for different wavelengths and core radii for the first three modes were also studied. In all cases, we got the higher values when the wavelengths are small the value, and then these values begin to reduction at increasing wavelength.

Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization

In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization

In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

A new mathematical program with complementarity constraints for optimal localization of pressure reducing valves in water distribution systems

Water loss reduction in water distribution systems (WDSs) is a challenging task for water utilities worldwide. One of the most reliable and cost-effective ways to reduce water loss is to properly regulate operational pressure of the system through optimizing pressure reducing valve (PRV) placements. This well-known engineering problem can be casted into a mixed-integer nonlinear program (MINLP) where binary variables are introduced to represent positions of PRVs. Many works in the literature applied heuristic algorithms to address the optimization problem. In this paper, at first, we proposed a new optimization model and reformulated it as the mathematical program with complementarity constraints (MPCCs). It is due to the fact that the stationary point of the MPCCs is likely to be trapped into bad local solutions, a soft heuristic method is then proposed to determine the MINLP local solution in each iteration before a stationary point of the MPCCs is reached. This method not only enhances the quality of MINLP solution, but also decreases computation time for solving the MPCCs. The newly formulated MPCCs is applied to determine optimal localization of PRVs for two WDS benchmarks and a real-world WDS in Vietnam. The results are compared with others in the literature demonstrating that using our new optimization model, better and more reliable MINLP solution can be found for large scale WDSs.

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

Changes in the end part of the QRS complex and the ST-T segment in patients with coronavirus infection

This article is devoted to the patterns of changes in the QRS complex and the ST-T segment in patients with a new coronavirus infection. The article presents the results of a comparison of electrocardiogram data in 70 patients with COVID-19 who were treated in 1st Department of Internal Medicine Postgraduate Training from April to July 2020. Each patient had at least two electrocardiograms taken (at the beginning and at the end of the disease). In the course of the work, a new method for measuring the area of the teeth P, T, QRS complex and ST-T segment was developed and described using the dynamic mathematical program GeoGebra Classic 6.0 by correlating the millimeter grids of the electrocardiogram and the program and further constructing an irregular shape taking into account the polarity of the teeth and segments. According to the study, the sum of the ST-T segment areas in all 12 leads is statistically significantly greater at the end of the disease in individuals over 30 years old. It is also significantly higher in the right thoracic leads (V1-V2) in for all ages. Probably, these changes are associated with the severity of the underlying disease and, consequently, with the overload of the right parts of the heart.