A trust region strategy for nonlinear equality constrained optimization. (English) Zbl 0566.65048

Celis, M. R.; Dennis, J. E.; Tapia, R. A.

Numerical optimization, Proc. SIAM Conf., Boulder/Colo. 1984, 71-82 (1985).

[For the entire collection see Zbl 0552.00011.]
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 \(L_ 2\)-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).

Reviewer: K.Schittkowski

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming

Keywords:

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

Citations:

Zbl 0552.00011