Adaptive Learning-Enhanced Convex Optimization for Energy-Efficient Cloud Resource Scheduling

Cloud computing infrastructure faces unprecedented energy consumption challenges, with data centers accounting for approximately 3% of global electricity usage. This paper presents an adaptive learning-enhanced convex optimization framework that integrates neural network-based parameter learning with traditional mathematical optimization to address dynamic cloud resource scheduling. The proposed approach formulates resource allocation as a convex optimization problem with energy efficiency objectives, employing adaptive step size and momentum strategies guided by learned workload patterns. Neural networks predict optimal Lagrangian multipliers and optimization parameters from historical scheduling data, reducing convergence iterations by 60.7% compared to traditional solvers. Experimental evaluation on real-world workload traces demonstrates energy efficiency improvements of 31.7% while maintaining quality-of-service constraints. The framework achieves theoretical convergence guarantees through KKT conditions while adapting to dynamic workload variations, providing a mathematically rigorous yet practically efficient solution for sustainable cloud computing.