Nadezhda Ribarska

A Pontryagin Maximum Principle for Infinite-Dimensional Problems

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 to prove the main result of the present paper—a Pontryagin maximum principle for infinite-dimensional optimal control problems with pointwise terminal constraints in arbitrary Banach state space. By refining the classical variational technique we are able to replace the differentiability of the norm of the state space (guaranteed by the strict convexity of its dual norm, which is assumed in the known results) by a separation argument. We also drop another key assumption which is common in the existing literature on infinite-dimensional control problems—that the set of variations (in the state space) of the state trajectorys endpoint (resulting from the control variations) be finite-codimensional. Instead, we require only that it has nonempty interior in its closed affine hull. As an application of the abstract result we present an illustrative example—an optimal control problem for an age-structured system with pointwise terminal state constraints.

On the Existence of Solutions to Differential Inclusions with Nonconvex Right-Hand Sides

We study the existence of solutions of differential inclusions with upper semicontinuous right-hand sides. The investigation was prompted by the well-known Filippov examples. We define a new concept, “colliding on a set.” In the case when the admissible velocities do not “collide” on the set of discontinuities of the right-hand side, we expect that at least one trajectory emanates from every point. If the velocities do “collide” on the set of discontinuities of the right-hand side, the existence of solutions is not guaranteed, as is seen from one of Filippovs examples. In this case we impose an additional condition in order to prove the existence of a solution starting at a point of the discontinuity set. For the right-hand sides under consideration, we assume the following: whenever the velocities “collide” on a set

Nonseparation of Sets and Optimality Conditions

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A Functional Analytic Approach to a Bolza Problem

there exist tangent velocities (belonging to the Clarke tangent cone to

ON A QUESTION OF J.BORWEIN AND H.WIERSMA

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Internal characterization of fragmentable spaces

) on a dense subset of

SPECULATING ABOUT MOUNTAINS

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Critical point theory for vector valued functions

. Then we prove the existence of an

A stability property for locally uniformly rotund renorming

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A note on “on a critical point theory for multivalued functionals and application to partial differential inclusions

-solution for every