On the Convergence of Successive Linear-Quadratic Programming Algorithms

Authors:
Richard H. Byrd;Nicholas I. M. Gould;Jorge Nocedal;Richard A. Waltz
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Optimization
Year:
2005

Citing 0
Cited 6

Steering exact penalty methods for nonlinear programming

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Abstract

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 et al. [Math. Program., 100 (2004), pp. 27--48]. 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.