title: Trust-Search Methods for Large-Scale Optimization abstract: Recent research on interior methods has re-emphasized the role of sequential unconstrained optimization for the solution of very large nonconvex problems. However, existing line-search and trust-region methods for unconstrained optimization may get into difficulty near points at which the Hessian is singular. In such cases, line-search methods may require many iterations to converge, and trust-region methods may require many iterations to solve the constrained subproblem. A new class of methods is proposed that combines the best features of trust-region and line-search methods. These ``trust-search'' methods maintain the rapid convergence associated with trust-region methods while solving the subproblem at a cost comparable to that of a line-search method. (This work is joint with Julia Kroyan.) Philip E. Gill University of California, San Diego La Jolla, CA