Geodesic
Robust optimization: stabilization methods and well-posedness in mathematical programming and saddle point problems
Serdica Mathematical Journal, Tome 44 (2018) no. 3-4, pp. 243-302.

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In this paper, we provide various characterizations of several well-posedness concepts in mathematical programming and saddle point problems. We introduce a large class of generalized stabilization methods and display variational asymptotic developments of minimum and saddle values of regularization schemes under consideration. The convex and nonconvex cases are studied. A class of well-posed problems has been also studied using infimal-convolution, epigraphical analysis and subdifferentiability. Many examples and applications illustrated our investigation. Notably an application to Legendre-Fenchel transform in locally convex spaces is given. A detailed study of Levitin-Polyak well-posedness in mathematical programming as well as the one for saddle point problems have been displayed in metric and normed spaces.
Keywords: generalized stabilization methods, well-posed optimization problems, variational asymptotic developments, conjugacy, stability, α-convexity, epi-convergence, convex-concave functions, subdifferentiability, infimal-convolution, well-posed saddle point problems and variational sets, saddle functions, 49K40, 49J45, 49L25, 49J52, 90C26, 90C31 
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     author = {Mentagui, Driss},
     title = {Robust optimization: stabilization methods and well-posedness in mathematical programming and saddle point problems},
     journal = {Serdica Mathematical Journal},
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     volume = {44},
     number = {3-4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2018_44_3-4_a0/}
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Mentagui, Driss. Robust optimization: stabilization methods and well-posedness in mathematical programming and saddle point problems. Serdica Mathematical Journal, Tome 44 (2018) no. 3-4, pp. 243-302. http://geodesic.mathdoc.fr/item/SMJ2_2018_44_3-4_a0/