A natural Hessian approximation for ensemble based optimization

Abstract A key challenge in reservoir management and other fields of engineering involves optimizing a nonlinear function iteratively. Due to the lack available gradients commercial simulators attention over last decades has been on gradient free methods or approximations. In particular, ensemble-based optimization gained popularity decade due its simplicity efficient implementation when considering an ensemble models. Typically, regression type approximation is used backtracking line search setting. This paper introduces Hessian utilizing Monte Carlo natural with respect covariance matrix. can further be implemented trust region approach order improve efficiency algorithm. The advantages using such approximations are demonstrated by testing proposed algorithm Rosenbrock synthetic field.