Steering Exact Penalty Methods for Optimization

This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linear-quadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods. Department of Computer Science, University of Colorado, Boulder, CO 80309. This author was supported by Army Research Office Grants DAAD19-02-1-0407, and by National Science Foundation grants CCR-0219190 and CHE-0205170. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, 60208-3118, USA. These authors were supported by National Science Foundation grant CCR-0219438 and Department of Energy grant DE-FG02-87ER25047-A004.