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On regularity estimates for mappings between embedded manifolds

Ioffe A.

Control and Cybernetics

2007

Vol. 36, no 3

659-668

We describe a class of metric spaces such that for set-valued mappings into such spaces it is possible to give a precise expression of regularity moduli in terms of slopes of DeGiorgi-Marino-Tosques. We also show that smooth manifolds in Banach spaces endowed with the induced metric belong to this class.

On necessary conditions in variable end-time optimal control problems

Ioffe A.

Control and Cybernetics

2005

Vol. 34, no 3

805-817

The paper contains a new necessary optimality condition for optimal control problems with free terminal time and discontinuous time dependence, which, actually is a family of conditions, each corresponding to a continuation of optimal trajectory beyond the optimal time for an arbitrary small interval.

Convergence and extensions of variational problems with non-coercive functionals

Ioffe A.

Control and Cybernetics

2002

Vol. 31, no 3

507-519

The paper is a transcript of the lecture given at the European Symposium on Well-Posedness in Optimization in Warsaw. It contains a complete theory of variational problems with integrands not depending on x, including existence and relaxation theorems, a complete description of solutions and the connection between variational convergences of functionals and convergence of value functions and solutions of associated variational problems with the main emphasis on functionals that lack coercivity.