Randomized Simplicial Hessian Update

Recently, a derivative-free optimization algorithm was proposed that utilizes minimum Frobenius norm (MFN) Hessian update for estimating the second derivative information, which in turn is used accelerating search. The formula relies only on computed function values and closed-form expression special case of more general approach first published by Powell. This paper analyzes convergence under assumption points from Rn where value known are random. analysis assumes N+2 obtained adding N+1 vectors to central point. transforming prototype set with random orthogonal matrix Haar measure. must positively span N?n dimensional subspace. Because nature we can estimate lower bound expected improvement approximate Hessian. derived Leventhal Lewis. We generalize their result show amount greatly depends N as well choice set. then analyzing performance based various commonly sets. One results this states regular n-simplex bad because it does not guarantee any