Abstract

Typical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on Γ\Gamma-convergence of the corresponding functionals usually rely on equi-coercivity assumptions. Without them the connection between the Γ\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 Γ\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)

Author information

Contact details are reproduced from the original publication and may be historical.

Lorenzo Freddi

Dip. di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy

freddi@dimi.uniud.it

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Suggested citation

L. Freddi, A. D. Ioffe. “On Limits of Variational Problems. The Case of a Non-Coercive Functional.” Journal of Convex Analysis 9 (2002), No. 2, 439–462. https://doi.org/10.68381/jca09026

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.