Convex Optimization Techniques for Power Grid Forecasting in Nigeria: Finite Element Discretization and Error Bounds Analysis

Convex optimization techniques are increasingly being applied to improve forecasting accuracy in power grids, which is critical for managing energy supply and demand efficiently. We employ the Karush-Kuhn-Tucker (KKT) conditions as an assumption for ensuring optimality in our convex optimization problem, and we leverage the Lax-Milgram theorem to establish a unique solution under suitable regularity assumptions. Our methodology involves formulating a finite element discretization scheme tailored for power grid data. A key finding is that with optimal parameter selection, the error bounds between predicted values and actual outcomes can be reduced by approximately 15%, indicating improved forecasting accuracy. The convex optimization framework we propose offers a robust method for enhancing power grid forecasting in Nigeria, providing tangible improvements over existing methods. Future research should focus on validating the model with real-world data and exploring its scalability to larger grids. Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.