
Characterizations of the solution set for nonessentially quasiconvex programmingCharacterizations of the solution set for nonessentially quasiconvex programmingAA12249544 
"/Suzuki, Satoshi/"Suzuki, Satoshi ,
"/Kuroiwa, Daishi/"Kuroiwa, Daishi
11
(
8
)
, pp.1699

1712 , 201712 , SpringerVerlag
ISSN:18624472
NII書誌ID(NCID):AA12249544
内容記述
Characterizations of the solution set in terms of subdifferentials play an important role in research of mathematical programming. Previous characterizations are based on necessary and sufficient optimality conditions and invariance properties of subdifferentials. Recently, characterizations of the solution set for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential are studied by the authors. Unfortunately, there are some examples such that these characterizations do not hold for nonessentially quasiconvex programming. As far as we know, characterizations of the solution set for nonessentially quasiconvex programming have not been studied yet. In this paper, we study characterizations of the solution set in terms of subdifferentials for nonessentially quasiconvex programming. For this purpose, we use Martínez–Legaz subdifferential which is introduced by Martínez–Legaz as a special case of csubdifferential by Moreau. We derive necessary and sufficient optimality conditions for quasiconvex programming by means of Martínez–Legaz subdifferential, and, as a consequence, investigate characterizations of the solution set in terms of Martínez–Legaz subdifferential. In addition, we compare our results with previous ones. We show an invariance property of Greenberg–Pierskalla subdifferential as a consequence of an invariance property of Martínez–Legaz subdifferential. We give characterizations of the solution set for essentially quasiconvex programming in terms of Martínez–Legaz subdifferential.
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