Geodesic
On Limits of Variational Problems. The Case of a Non-Coercive Functional
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 439-462
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Typical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on Gamma-convergence of the corresponding functionals usually rely on equi-coercivity assumptions. Without them the connection between the Gamma-limit of the functionals and values and/or solutions of the problems may be completely broken. The question to be discussed is whether it is possible, even in the absence of a coercivity-type assumption, to find limiting optimization problems (parametrized in a similar way and determined by functionals which may differ from the Gamma-limits of the functionals of the sequence) such that the value functions and solutions of the problems of the sequence converge in a certain sense to those of the limiting problems. A positive answer to the question is given to a class of variational problems (containing optimal control problems with linear dynamics). 
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     author = {L. Freddi and A. D. Ioffe},
     title = {On {Limits} of {Variational} {Problems.} {The} {Case} of a {Non-Coercive} {Functional}},
     journal = {Journal of convex analysis},
     pages = {439--462},
     year = {2002},
     volume = {9},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/}
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L. Freddi; A. D. Ioffe. On Limits of Variational Problems. The Case of a Non-Coercive Functional. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 439-462. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/