This research identifies conditions for penalty functions’ exactness in optimization, highlighting implications for unbounded constraints.
This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz or semi-algebraic is studied in detail. The conditions are given in terms of properties of the objective and residual functions of the problems in question. The obtained results generalize and improve some known results in the literature on exact penalty functions.
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Jiao et al. (2025) studied this question.
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