On the Convergence of Successive Linear-Quadratic Programming Algorithms

The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27–48, 2004). Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic models, respectively. It is shown that, for a fixed penalty parameter, the sequence of iterates approaches stationarity of the penalty function. A procedure for dynamically adjusting the penalty parameter is described, and global convergence results for it are established. Department of Computer Science, University of Colorado, Boulder, CO 80309. This author was supported by Army Research Office Grants DAAG55-98-1-0176 and DAAD19-02-1-0407, and NSF grants CCR0219190 and CHE-0205170. Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, England, EU. This author was supported by EPSRC grants GR/R46641 and GR/S42170. Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208-3118. These authors were supported by National Science Foundation grants ATM-0086579 and CCR-0219438, and by Department of Energy grant DE-FG02-87ER25047-A004.