Cloud Resource Allocation with Convex Optimization

We present a convex optimization framework for overcoming the limitations of Kubernetes Cluster Autoscaler by intelligently allocating diverse cloud resources while minimizing costs and fragmentation. Current Kubernetes scaling mechanisms are restricted to homogeneous scaling of existing node types, limiting cost-performance optimization possibilities. Our matrix-based model captures resource demands, costs, and capacity constraints in a unified mathematical framework. A key contribution is our logarithmic approximation to the indicator function, which enables dynamic node type selection while maintaining problem convexity. Our approach balances cost optimization with operational complexity through interior-point methods. Experiments with real-world Kubernetes workloads demonstrate reduced costs and improved resource utilization compared to conventional Cluster Autoscaler strategies that can only scale up or down existing node pools.