Non-Convex Distributed Optimization

We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results obtained previously to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function. Our analysis shows that this noised procedure converges at a rate of $O(1/t)$

An ensemble framework for day-ahead forecast of PV output in smart grids

The uncertainty associated with solar output power is a big challenge to design, manage and implement effective demand response and management strategies. Therefore, a precise PV output power forecast is an utmost importance to allow seamless integration and higher level of penetration. In this research, a neural network ensemble (NNE) scheme is proposed, which is based on particle swarm optimization (PSO) trained feedforward neural network (FNN). Five different FFN structures with 20 FNN in each structure with varying network parameters are used to achieve the diverse and accurate forecast results. These results are combined using trim aggregation after removing the upper and lower forecast error extremes. Correlated variables namely wavelet transformed output power of PV, solar irradiance, wind speed, temperature and humidity are applied as inputs of multivariate NNE. Clearness index is used to classify days into clear, cloudy and partially cloudy days. The forecast results demonstrate that the proposed framework improves the forecast accuracy significantly in comparison with individual and benchmark models