Search Results (6)

Home energy management systems (HEMS) aim to provide intelligent control of the thermal comfort inside smart buildings with the minimum energy cost, while satisfying the energy consumption requests and increasing the use of energy from renewable sources. The capabilities of these intelligent HEMS agents are restricted due to the personalized observability of the environment, resulting in limited knowledge gathering and potentially sub-optimal decisions. Furthermore, several buildings have recently been organized into small energy communities, with the ultimate goal of sharing intelligence between agents in federated learning schemes.In this context, we propose a personalized federated deep reinforcement learning method using Moreau envelopes (pFedMe) for joint energy cost and household comfort optimization in energy communities that consist of multiple smart homes. Specifically, a Twin-Delayed Deep Deterministic Policy Gradient (TD3) actor–critic model is introduced, dynamically observing the state of the smart home environment and suggesting control actions on the operation of the Energy Storage System and on the regulation of the indoor temperature. The TD3 actor–critic model leads to improved policy performance in the continuous control of these systems, mitigating the overestimation bias and improving the training stability of the intelligent agents. The efficiency of the proposed method is verified via simulations based on real data, achieving a beneficial trade-off between the energy cost and the thermal comfort compared to FedAvg and Fedprox baselines. The results show that the proposed pFedMe framework consistently outperforms FedAvg and FedProx in both convergence speed and overall reward, achieving an energy cost reduction of approximately 10% compared to the other schemes, while exhibiting marginal thermal comfort behavior. Full article

In this paper, we study a class of optimization problems with separable constraint structures, characterized by a combination of convex and nonconvex constraints. To handle these two distinct types of constraints, we introduce a partial augmented Lagrangian function by retaining nonconvex constraints while relaxing convex constraints into the objective function. Specifically, we employ the Moreau envelope for the convex term and apply second-order variational geometry to analyze the nonconvex term. For this partial augmented Lagrangian function, we study its saddle points and establish their relationship with KKT conditions. Furthermore, second-order optimality conditions are developed by employing tools such as second-order subdifferentials, asymptotic second-order tangent cones, and second-order tangent sets. Full article

We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We provide evidence of globally weak convergence and the fact that these algorithms can be equipped with relaxed and/or inertial steps, leading to improved convergence guarantees. Full article

In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment. Full article

In this paper, we present a novel variational wavelet inpainting based on the total variation (TV) regularization and the l1-norm fitting term. The goal of this model is to recover incomplete wavelet coefficients in the presence of impulsive noise. By incorporating the Moreau envelope, the proposed model for wavelet inpainting can better handle the non-differentiability of the l1-norm fitting term. A modified primal dual fixed-point algorithm is developed based on the proximity operator to solve the proposed variational model. Moreover, we consider the existence of solution for the proposed model and the convergence analysis of the developed iterative scheme in this paper. Numerical experiments show the desirable performance of our method. Full article

Hyperspectral images (HSIs) denoising aims at recovering noise-free images from noisy counterparts to improve image visualization. Recently, various prior knowledge has attracted much attention in HSI denoising, e.g., total variation (TV), low-rank, sparse representation, and so on. However, the computational cost of most existing algorithms increases exponentially with increasing spectral bands. In this paper, we fully take advantage of the global spectral correlation of HSI and design a unified framework named subspace-based Moreau-enhanced total variation and sparse factorization (SMTVSF) for multispectral image denoising. Specifically, SMTVSF decomposes an HSI image into the product of a projection matrix and abundance maps, followed by a ‘Moreau-enhanced’ TV (MTV) denoising step, i.e., a nonconvex regularizer involving the Moreau envelope mechnisam, to reconstruct all the abundance maps. Furthermore, the schemes of subspace representation penalizing the low-rank characteristic and ${\ell }_{2,1}$ -norm modelling the structured sparse noise are embedded into our denoising framework to refine the abundance maps and projection matrix. We use the augmented Lagrange multiplier (ALM) algorithm to solve the resulting optimization problem. Extensive results under various noise levels of simulated and real hypspectral images demonstrate our superiority against other competing HSI recovery approaches in terms of quality metrics and visual effects. In addition, our method has a huge advantage in computational efficiency over many competitors, benefiting from its removal of most spectral dimensions during iterations. Full article