Geodesic
Zero Duality Gap and Attainment with Possibly Non-Convex Data
Journal of convex analysis, Tome 23 (2016) no. 2, pp. 615-629
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A newly defined notion of convex closedness regarding a set is used in order to state a necessary and sufficient criterion for the min-sup property in non necessarily convex primal-dual optimization problems, generalizing well-known theorems valid in the convex setting. Our main result is then applied to the classical penalty method.
Classification : 49M30, 49N15, 52A20
Mots-clés : Dual optimization, min-sup property, convex closedness regarding a set, penalty method 
@article{JCA_2016_23_2_JCA_2016_23_2_a11,
     author = {E. Ernst and M. Volle},
     title = {Zero {Duality} {Gap} and {Attainment} with {Possibly} {Non-Convex} {Data}},
     journal = {Journal of convex analysis},
     pages = {615--629},
     year = {2016},
     volume = {23},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_2_JCA_2016_23_2_a11/}
}
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E. Ernst; M. Volle. Zero Duality Gap and Attainment with Possibly Non-Convex Data. Journal of convex analysis, Tome 23 (2016) no. 2, pp. 615-629. http://geodesic.mathdoc.fr/item/JCA_2016_23_2_JCA_2016_23_2_a11/