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Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. (English) Zbl 1038.90076
An SQP globally convergent algorithm for solving nonlinear $C^2$-optimization problems with equality and inequality constraints is presented. The algorithm is based on trust region methods where filters are used instead of penalty functions. The filter concept was introduced by {\it R. Flechter} and {\it S. Leyffer} [Nonlinear programming without a panelty function, Math. Program. 91, 239--269 (2002; Zbl 1049.90088)]. It aims to avoid steps that are no improvement w.r.t. feasibility and objective value. Another feature of the algorithm is that the steps of the quadratic trust region subproblems are viewed as the sum of a normal step (for satisfying the constraints) and a tangential step (for reducing the objective function model of the subproblem). Therefore it is not required that the solution of the quadratic subproblems are determinied exactly.

90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
90C55Methods of successive quadratic programming type
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