Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. We develop a new piecewise linear convex regression method that uses the Convex Adaptive Partitioning (CAP) estimator in an ensemble setting, Ensemble Convex Adaptive Partitioning (E-CAP). The ensembles alleviate some problems associated with convex piecewise linear estimators, such as instability when used to approximate constraints or objective functions for optimization, while maintaining desirable properties, such as consistency and O(n log(n)^2) computational complexity. We empirically demonstrate that E-CAP outperforms existing convex regression methods both when used for prediction and optimization. We then apply E-CAP to device modeling and constraint approximation for geometric programming based circuit design.