Using continuous Gaussian aggregation, 3D Gaussian Splatting (3DGS) provides an effective representation of scene geometry for novel view synthesis. Despite high-quality and real-time rendering, its large number of primitives causes significant memory overhead, limiting deployment on low-power or edge devices. To address this, we propose SplatOpt, an optimization-guided framework that introduces sparsity constraints during training. By formulating simplification as a constrained optimization problem, SplatOpt uses ADMM-based alternating optimization to reduce the number of Gaussians while preserving visual fidelity. To further enhance spatial structure, we introduce Geometry-Aligned Split, a deterministic densification strategy that partitions Gaussians along principal axes, improving coherence and training stability. We also implement CUDA-based acceleration for gradient aggregation and perceptual loss computation, improving efficiency on resource-limited hardware. Experiments show that SplatOpt removes over 80% of Gaussians while maintaining or improving rendering quality. The resulting sparse representation supports efficient hardware rasterization and achieves approximately 3 \(\times \) higher frame rates than Vanilla 3DGS on lightweight GPUs, offering a robust and scalable solution for real-time rendering on constrained platforms.