Bahlali, Seid Necessary and sufficient optimality conditions for relaxed and strict control problems. (English) Zbl 1167.49024 SIAM J. Control Optim. 47, No. 4, 2078-2095 (2008). Summary: We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear stochastic differential equation, in which the control enters both the drift and the diffusion coefficients. By introducing a new approach, we establish necessary as well as sufficient conditions of optimality for two models. The first concerns the relaxed controls, which are measure-valued processes in which an optimal solution exists. The second is a particular case of the first and relates to strict control problems. These results are given in the form of global stochastic maximum principle by using only the first-order expansion and the associated adjoint equation. This improves all of the previous works on the subject. Cited in 16 Documents MSC: 49K45 Optimality conditions for problems involving randomness 93E20 Optimal stochastic control 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 93C10 Nonlinear systems in control theory Keywords:stochastic differential equation; strict control; relaxed control; maximum principle; adjoint process; variational inequality PDFBibTeX XMLCite \textit{S. Bahlali}, SIAM J. Control Optim. 47, No. 4, 2078--2095 (2008; Zbl 1167.49024) Full Text: DOI arXiv