Speaking of bound results, interval arithmetic comes to my mind and the work of Ulrich Kulisch [0]. I've used it together with automatic differentiation with so

Speaking of bound results, interval arithmetic comes to my mind and the work of Ulrich Kulisch [0]. I've used it together with automatic differentiation with some remarkable results, but the problems were comparably small (approx. 40 dimensional optimization). [0] http://www.math.kit.edu/ianm2/~kulisch/de http://www.math.kit.edu/ianm2/~kulisch/de