On the convexity of integrals of multivalued mappings. Applications in control theory
Using the notion of the local convexity index, we characterize in a quantitative way the local convexity of a set in the n-dimensional Euclidean space, defined by an integral of a multivalued mapping. We estimate the rate of convergence of the conditional gradient method for solving an abstract optimization problem by means of the convexity index of the constraining set at the solution point. These results are applied to the qualitative analysis of the solutions of time-optimal and Mayer problems for linear control systems, as well as for estimating the convergence rate of algorithms solving these problems.
scientific article; zbMATH DE number 3960383