A trust region algorithm for equality constrained optimization.

*(English)*Zbl 0816.90121An iterative technique for solving equality constrained nonlinear optimization problems is considered. In each step a search direction from an approximate solution is calculated by solving a quadratic programming subproblem which approximates the original problem. In an earlier paper [ibid. 35, No. 3, 265–278 (1986; Zbl 0598.90079)] the authors proposed an algorithm in which the step-length of each iteration is determined by means of a differentiable exact penalty function. The present paper extends the results to the case where convergence is forced by means of trust regions instead of line searches. Basically, in each iteration a trial step (bounded by a positive parameter) in the search direction is subjected to tests before being accepted. Global convergence properties and a local superlinear convergence result are proved.

##### MSC:

90C30 | Nonlinear programming |

65K10 | Numerical optimization and variational techniques |

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

49M30 | Other numerical methods in calculus of variations (MSC2010) |

##### Keywords:

global convergence properties; equality constrained nonlinear optimization; quadratic programming subproblem; trust regions; local superlinear convergence
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\textit{M. J. D. Powell} and \textit{Y. Yuan}, Math. Program. 49, No. 2 (A), 189--211 (1990; Zbl 0816.90121)

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##### References:

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