TRICE
swMATH ID:  5197 
Software Authors:  Dennis, J.E.; Heinkenschloss, Matthias; Vicente, Lu'{i}s N. 
Description:  Trustregion interiorpoint SQP algorithms for a class of nonlinear programming problems A family of trustregion interiorpoint 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.par 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 {it T. F. Coleman} and {it Y. Li} [SIAM J. Optim. 6, 418445 (1996; Zbl 0855.65063)] and they exploit trustregion techniques for equalityconstrained optimization. Thus, they allow the computation of the steps using a variety of methods, including many iterative techniques.par Global convergence of these algorithms to a firstorder KarushKuhnTucker (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 secondorder 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.par Numerical results for the solution of an optimal control problem governed by a nonlinear heat equation are reported. 
Homepage:  http://www.caam.rice.edu/~trice/ 
Keywords:  nonlinear programming; SQP methods; trustregion methods; interiorpoint algorithms; DikinKarmarkar ellipsoid; ColemanLi affine scaling; simple bounds; optimal control problems 
Related Software:  LANCELOT; Ipopt; SNOPT; CUTEr; TRON; NPSOL; LOQO; LSQR; ipfilter; SifDec; NewtonLib; LBFGS; CUTE; QSDPNAL; HSolver; PENLAB; z3; LMIRank; Benchmarks; RSOLVER 
Cited in:  46 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Trustregion interiorpoint SQP algorithms for a class of nonlinear programming problems. Zbl 0921.90137 Dennis, J. E.; Heinkenschloss, Matthias; Vicente, Luís N. 
1998

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Cited by 85 Authors
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Cited in 24 Serials
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