"On the Convergence of Successive Linear Programming Algorithms"
R. Byrd, N. Gould, J. Nocedal, R. Waltz.
SIAM J. Optimization, Vol. 16, No. 2, pp.471-489 (2005).
The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successsive 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.