DigitalCommons@WayneState

Title

Well-Posedness of Minimal Time Problem with Constant Dynamics in Banach Spaces

Authors

Giovanni Colombo, Università di Padova, ItalyFollow
Vladimir V. Goncharov, Universidade de Évora, PortugalFollow
Boris S. Mordukhovich, Wayne State UniversityFollow

Document Type

Technical Report

Abstract

This paper concerns the study of a general minimal time problem with a convex constant dynamic and a closed target set in Banach spaces. We pay the main attention to deriving efficient conditions for the major well-posedness properties that include the existence and uniqueness of optimal solutions as well as certain regularity of the optimal value function with respect to state variables. Most of the results obtained are new even in finite-dimensional spaces. Our approach is based on advanced tools of variational analysis and generalized differentiation.

Number in Series

2009.12

Disciplines

Applied Mathematics | Mathematics

AMS Subject Classification

49J53; 49J52; 46B20; 49J50

Comments

Dedicated to Jean-Baptiste Hiriart-Urruty in honor of his 60th birthday. This work was partially supported by M.I.U.R., project "Viscosity, Metric, and Control Theoretic Methods for Nonlinear Partial Differential Equations" and by CARIPARO "Visiting Professors' Program"; and by the US National Science Foundation under grant DMS-0603846

Recommended Citation

Colombo, Giovanni; Goncharov, Vladimir V.; and Mordukhovich, Boris S., "Well-Posedness of Minimal Time Problem with Constant Dynamics in Banach Spaces" (2009). Mathematics Research Reports. 71.
https://digitalcommons.wayne.edu/math_reports/71