Guigue, A. Set-valued return function and generalized solutions for multiobjective optimal control problems (MOC). (English) Zbl 1273.49022 SIAM J. Control Optim. 51, No. 3, 2379-2405 (2013). Summary: In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is defined in terms of a pointed convex cone containing the origin, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function \(V\) and provide a unique characterization for \(V\) in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton-Jacobi equation for single objective optimal control problems. Cited in 4 Documents MSC: 49J53 Set-valued and variational analysis 49K15 Optimality conditions for problems involving ordinary differential equations 49L20 Dynamic programming in optimal control and differential games 54C60 Set-valued maps in general topology 90C29 Multi-objective and goal programming Keywords:multiobjective optimal control; generalized Pareto optimality; dynamic programming; set-valued maps; contingent derivative; coderivative PDFBibTeX XMLCite \textit{A. Guigue}, SIAM J. Control Optim. 51, No. 3, 2379--2405 (2013; Zbl 1273.49022) Full Text: DOI arXiv