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Zbl 0566.65048
Celis, M.R.; Dennis, J.E.; Tapia, R.A.
A trust region strategy for nonlinear equality constrained optimization. (English)
[A] Numerical optimization, Proc. SIAM Conf., Boulder/Colo. 1984, 71-82 (1985).

[For the entire collection see Zbl 0552.00011.] \par The authors propose a trust region method for solving the equality constrained nonlinear programming problems. In each step, a certain subproblem is formulated and solved. The objective function could be a quadratic approximation of the original objective function or of the Lagrange function, where the constraints are obtained by bounding the step size and a linear constraint approximation in the $L\sb 2$-norm. Relationships of the trust region method with penalty or augmented Lagrangian functions and the sequential quadratic programming method are shown. A few comparative numerical results are presented based on an experimental implementation of the method and a standard SQP-code (VFO2AD).
[K.Schittkowski]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming

Keywords: nonlinear constrained optimization; global convergence; quadratic programming subproblem; SQP-method; trust region method; numerical results

Citations: Zbl 0552.00011

Cited in: Zbl 1187.90290 Zbl 1088.65049 Zbl 1080.65048 Zbl 0957.65060 Zbl 0773.90056 Zbl 0725.65061

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