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Appl Math Optim 2020 6;81(3):1021-1054. Epub 2018 Oct 6.

Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria.

The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. Read More

Appl Math Optim 2015;71(3):379-410

Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland.

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. Read More