Trust-region interior-point SQP algorithms for a class of nonlinear programming problems

被引:75
作者
Dennis, JE [1 ]
Heinkenschloss, M
Vicente, LN
机构
[1] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA
[2] Univ Coimbra, Dept Matemat, P-3000 Coimbra, Portugal
关键词
nonlinear programming; SQP methods; trust-region methods; interior-point algorithms; Dikin-Karmarkar ellipsoid; Coleman-Li affine scaling; simple bounds; optimal control problems;
D O I
10.1137/S036012995279031
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, a family of trust-region interior-point sequential quadratic programming (SQP) algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise, e.g., from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed, for a different class of problems, by Coleman and Li [SIAM J. Optim., 6 (1996), pp. 418-445] and they exploit trust-region techniques for equality-constrained optimization. Thus, they allow the computation of the steps using a variety of methods, including many iterative techniques. Global convergence of these algorithms to a first-order Karush-Kuhn-Tucker (KKT) limit point is proved under very mild conditions on the trial steps. Under reasonable, but more stringent, conditions on the quadratic model and on the trial steps, the sequence of iterates generated by the algorithms is shown to have a limit point satisfying the second-order necessary KKT conditions. The local rate of convergence to a nondegenerate strict local minimizer is q-quadratic. The results given here include, as special cases, current results for only equality constraints and for only simple bounds. Numerical results for the solution of an optimal control problem governed by a nonlinear heat equation are reported.
引用
收藏
页码:1750 / 1794
页数:45
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