adaptive cubic regularization methods have several favorable properties for nonconvex optimization. in particular, under mild assumptions, they are globally convergent to a second-order stationary point. in this talk, i will introduce an adaptive cubic regularization method for unconstrained optimization. methods analogous to those used to solve the trust-region subproblem will be discussed for solving the local cubic model. some numerical results will be presented that compare a cubic regularized newton's method, a standard trust-region method and a trust-search method.