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On Optimality Conditions via Weak Subdifferential and Augmented Normal Cone
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Ali Farajzadeh   , Parisa Cheraghi |
| Razi University of Kermanshah , farajzadehali@gmail.com |
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Abstract: (7302 Views) |
| In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator function. Relation between weak subifferential and augmented normal cone and epigraph is also explored. We also obtain optimality conditions via weak subdifferential and augmented normal cone. Finally, we define the Stampacchia and Minty solution via weak subdifferential and investigate the relation between Stampacchia and Minty solution and the minimal point. |
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| Keywords: Subgradient, Weak subgradient, Normal cone, Augmented normal cone, Frechet differentiable function, Locally Lipchitz function. |
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Full-Text [PDF 275 kb]
(12613 Downloads)
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Type of Study: Original |
Subject:
Continuous Optimization
Received: 2019/12/5 | Accepted: 2019/12/5 | Published: 2019/12/5
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