A trust region method for constrained nonsmooth equations.

*(English)*Zbl 0813.65091
Hager, W. W. (ed.) et al., Large scale optimization. State of the art. Papers presented at the conference, held February 15-17, 1993 at the University of Florida, Gainesville, FL, USA. Dordrecht: Kluwer Academic Publishers. 155-181 (1994).

A trust region algorithm for solving a system of nonsmooth equations subject to linear constraints is developed. This method is based on the trust region idea for solving smooth equation and unconstrained optimization problems and involves the solution of a sequence of problems defined by an iteration function. Special attention is paid to the question of when the “critical points” of the nonsmooth optimization formulation are solutions of the original equations.

Applications of the specialization of the method (an arbitrary – norm trust region method) to complementarity problems are considered, in particular, for solving a spatial price equilibrium model. Sequential convergence of the method and its rate of convergence are established and a few computational results are given.

For the entire collection see [Zbl 0795.00025].

Applications of the specialization of the method (an arbitrary – norm trust region method) to complementarity problems are considered, in particular, for solving a spatial price equilibrium model. Sequential convergence of the method and its rate of convergence are established and a few computational results are given.

For the entire collection see [Zbl 0795.00025].

Reviewer: O.Vaarmann (Tallinn)

##### MSC:

65K05 | Numerical mathematical programming methods |

90C30 | Nonlinear programming |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

##### Keywords:

critical points; trust region algorithm; nonsmooth optimization; complementarity problems; price equilibrium model; convergence; computational results
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\textit{S. A. Gabriel} and \textit{J.-S. Pang}, in: Large scale optimization. State of the art. Papers presented at the conference, held February 15-17, 1993 at the University of Florida, Gainesville, FL, USA. Dordrecht: Kluwer Academic Publishers. 155--181 (1994; Zbl 0813.65091)

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