## An Improved Cutting Plane Method for Convex Optimization, Convex-Concave Games and its Applications

We prove that, unconditionally, for all constants a, NQP = NTIME[n^polylog(n)] cannot be (1/2 + 2^(-log^a n) )-approximated by 2^(log^a n)-size ACC^0 circuits. Previously, it was even open whether E^NP can be (1/2+1/sqrt(n))-approximated by AC^0[2] circuits. As a straightforward application, we obtain an infinitely often non-deterministic pseudorandom generator for poly-size ACC^0 circuits with seed length 2^{log^eps n}, for all eps > 0.