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On sequential optimality conditions for smooth constrained optimization. (English) Zbl 1225.90123
Summary: Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate Karush-Kuhn-Tucker and approximate gradient projection conditions are analysed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed.

MSC:
90C30 Nonlinear programming
49K99 Optimality conditions
65K05 Numerical mathematical programming methods
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