2020
DOI: 10.48550/arxiv.2008.03158
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A sequential optimality condition for Mathematical Programs with Cardinality Constraints

Abstract: In this paper we propose an Approximate Weak stationarity (AW -stationarity) concept designed to deal with Mathematical Programs with Cardinality Constraints (MPCaC), and we proved that it is a legitimate optimality condition independently of any constraint qualification. Such a sequential optimality condition improves weaker stationarity conditions, presented in a previous work. Many research on sequential optimality conditions has been addressed for nonlinear constrained optimization in the last few years, s… Show more

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Cited by 2 publications
(2 citation statements)
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“…And [19] proposed a cone-continuity constraint qualification. At the same time, [14] defines the first-order stationarity concept of the relaxation problem, called CC-Strong-stationary (CC-S-stationary) and CC-Mordukhovich-stationary (CC-M-stationary), where CC-S-stationary is equivalent to the Karush-Kuhn-T ucker (KKT) condition of the relaxation problem, and the CC-M-stationary is equivalent to the KKT condition of T N LP (x * ); [21] provides a Weak-type stationarity. It is worth mentioning that, unlike CC-S-stationary and Weak-type stationarity, CC-M-stationary is only related to the original variable x, and [18] proves that CC-S-stationary and CC-M-stationary are equivalence in the original variable space.…”
Section: Introductionmentioning
confidence: 99%
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“…And [19] proposed a cone-continuity constraint qualification. At the same time, [14] defines the first-order stationarity concept of the relaxation problem, called CC-Strong-stationary (CC-S-stationary) and CC-Mordukhovich-stationary (CC-M-stationary), where CC-S-stationary is equivalent to the Karush-Kuhn-T ucker (KKT) condition of the relaxation problem, and the CC-M-stationary is equivalent to the KKT condition of T N LP (x * ); [21] provides a Weak-type stationarity. It is worth mentioning that, unlike CC-S-stationary and Weak-type stationarity, CC-M-stationary is only related to the original variable x, and [18] proves that CC-S-stationary and CC-M-stationary are equivalence in the original variable space.…”
Section: Introductionmentioning
confidence: 99%
“…However, there are still very few relevant results about CCOP. [21] establishes a sequential optimality condition, called CC-approximate weak stationarity (CC-AW-stationarity), but this condition is based on the (x, y) space. Therefore, Kanzow et al [19] proposed CC-approximate Mordukhovich stationarity (CC-AM-stationarity), which is only related to x, and a proof is given that it is equivalent to CC-AWstationary.…”
Section: Introductionmentioning
confidence: 99%