Search results for "Mathematical optimization"
showing 10 items of 1300 documents
A Deep Reinforcement Learning scheme for Battery Energy Management
2020
Deep reinforcement learning is considered promising for many energy cost optimization tasks in smart buildings. How-ever, agent learning, in this context, is sometimes unstable and unpredictable, especially when the environments are complex. In this paper, we examine deep Reinforcement Learning (RL) algorithms developed for game play applied to a battery control task with an energy cost optimization objective. We explore how agent behavior and hyperparameters can be analyzed in a simplified environment with the goal of modifying the algorithms for increased stability. Our modified Deep Deterministic Policy Gradient (DDPG) agent is able to perform consistently close to the optimum over multi…
Applications and numerical convergence of the partial inverse method
2006
In 1983, J.E. Spingarn introduced what he called the Partial Inverse Method in the framework of Mathematical Programming. Since his initial articles, numerous applications have been given in various fields including Lagrangian multipliers methods, location theory, convex feasibility problems, analysis of data, economic equilibrium problems. In a first part of this paper we give a survey of these applications. Then by means of optimization problems relevant to location theory such as single and multifacility minimisum or minimax location problems, we examine the main advantages of the algorithm and we point out its drawbacks mainly concerning the rate of convergence. We study how different p…
A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges
2015
In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…
A novel numerical meshless approach for electric potential estimation in transcranial stimulation
2015
In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.
Unbiased Simultaneous Prediction Limits on Observations in Future Samples
2013
This paper provides procedures for constructing unbiased simultaneous prediction limits on the observations or functions of observations of all of k future samples using the results of a previous sample from the same underlying distribution belonging to invariant family. The results have direct application in reliability theory, where the time until the first failure in a group of several items in service provides a measure of assurance regarding the operation of the items. The simultaneous prediction limits are required as specifications on future life for components, as warranty limits for the future performance of a specified number of systems with standby units, and in various other app…
Online pricing for demand-side management in a low-voltage resistive micro-grid via a Stackelberg game with incentive strategies
2022
It has been demonstrated that online pricing mechanisms are a viable solution for demand side management in power systems. This study deals with the analysis and design of a droop-controlled low-voltage resistive AC micro-grid network system. Such a system is subjected to a dynamic demand obtained from an online pricing mechanism, which is proposed as a novelty in the study of micro-grids. This mechanism is derived from a variation of the Stackelberg game, which includes the use of incentive strategies. First, a configuration in which a supplier announces an incentive function and (Formula presented.) -consumers’ reaction to the resulting personalised price is presented. Then, a detailed st…
Well-Balanced Adaptive Mesh Refinement for shallow water flows
2014
Well-balanced shock capturing (WBSC) schemes constitute nowadays the state of the art in the numerical simulation of shallow water flows. They allow to accurately represent discontinuous behavior, known to occur due to the non-linear hyperbolic nature of the shallow water system, and, at the same time, numerically maintain stationary solutions. In situations of practical interest, these schemes often need to be combined with some kind of adaptivity, in order to speed up computing times. In this paper we discuss what ingredients need to be modified in a block-structured AMR technique in order to ensure that, when combined with a WBSC scheme, the so-called 'water at rest' stationary solutions…
The stability problem and noisy projections in discrete tomography
2004
Abstract The new field of research of discrete tomography will be described in this paper. It differs from standard computerized tomography in the reduced number of projections. It needs ad hoc algorithms which usually are based on the definition of the model of the object to reconstruct. The main problems will be introduced and an experimental simulation will prove the robustness of a slightly modified version of a well known method for the reconstruction of binary planar convex sets, even in case of projections affected by error. To the best of our knowledge this is one of the first experimental study of the stability problem with a statistical approach. Prospective applications include c…
Application of Graded Fuzzy Preconcept Lattices in Risk Analysis
2021
On the robust design of unknown inputs Takagi-Sugeno observer
2012
This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in Linear Matrix Inequalities (LMIs) terms. Relaxations are introduced by using intermediate variables. Numerical example is given to illustrate the effectiveness of the given result.