Maureen Doyle www.stanford.edu/~mdoyle Barrier Algorithms with Nonlinear Constraints. The most successful class of algorithms for nonconvex nonlinearly constrained optimization problems is sequential quadratic programming (SQP) methods. As the name suggests such methods solve a sequence of quadratic programs (QP). When second derivatives are available such QPs are in general nonconvex and this poses both technical and practical difficulties. For example, the QP may not have a solution and if it does it may not be unique. To circumvent the difficulties we proposed removing the inequality constraints using a barrier function. Such methods were first proposed in the 50s and have recently had a revival after their success in solving linear problems. They have been successfully extended to other convex problems although as yet how best to utilize the ideas for nonconvex nonlinearly constrained problems has still to be determined.