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- Mikhail Ivanov Krastanov, N. K. Ribarska, Ts. Y. Tsachev
- SIAM J. Control and Optimization
- 2011

Abstract. A basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable “needle-like control variations.” We use this idea it to prove the main result of the present paper—a Pontryagin maximum principle for infinite-dimensional optimal control problems with pointwise terminal constraints in… (More)

- Mikhail Ivanov Krastanov, N. K. Ribarska, Ts. Y. Tsachev
- SIAM Journal on Optimization
- 2007

- Mikhail Ivanov Krastanov, N. K. Ribarska
- SIAM J. Control and Optimization
- 2017

The definition of the weak slope of continuous functions introduced by Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness” of locally Lipschitz functions are discussed. A deformation lemma and a mountain pass theorem for usco mappings are proved. The relation between these results and the respective ones for lower… (More)

{ In this note we present a general mountain pass principle dropping any smoothness or even continuity assumptions on the functional. As a corollary, we prove existence of a point with an arbitrarily xed small slope if the "low" part of the "barrier" is suuciently far from the "boundary", obtaining in addition estimates for the location of the point.

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