3D Gaussian Splatting (3DGS) has emerged as a leading framework for novel view synthesis, yet its core optimization challenges remain underexplored. We identify two key issues in 3DGS optimization: entrapment in suboptimal local optima and insufficient convergence quality. To address these, we propose Opt3DGS, a robust framework that enhances 3DGS through a two-stage optimization process of adaptive exploration and curvature-guided exploitation. In the exploration phase, an Adaptive Weighted Stochastic Gradient Langevin Dynamics (SGLD) method enhances global search to escape local optima. In the exploitation phase, a Local Quasi-Newton Direction-guided Adam optimizer leverages curvature information for precise and efficient convergence. Extensive experiments on diverse benchmark datasets demonstrate that Opt3DGS achieves state-of-the-art rendering quality by refining the 3DGS optimization process without modifying its underlying representation.