Summary: On Sequential Optimality Conditions for smooth constrained
J. M. Mart´inez §
August 6, 2009.
Sequential optimality conditions provide adequate theoretical tools to justify stopping cri-
teria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Pro-
jection conditions are analyzed in this work. These conditions are not necessarily equivalent.
Implications between different conditions and counter-examples will be shown. Algorithmic
consequences will be discussed.
Key words: Nonlinear Programming, Optimality Conditions, Constraint Qualifications,
AMS Subject Classification: 90C30, 49K99, 65K05.
In this paper we study sequential first-order optimality conditions for Nonlinear Programming.
Necessary optimality conditions must be satisfied by the minimizers of optimization problems.
Usually, the theorems that support an optimality condition are of the form: "If the local minimizer
x satisfies CQ, then it satisfies KKT", where KKT represents the Karush-Kuhn-Tucker conditions