Summary
In this paper, we derive the necessary and sufficient conditions for optimal singular control for systems governed by general controlled McKean‐Vlasov differential equations, in which the coefficients depend on the state of the solution process as well as of its law and control. The control domain is assumed to be convex. The control variable has 2 components, ie, the first being absolutely continuous and the second being singular. The proof of our result is based on the derivative of the solution process with respect to the probability law and a corresponding Itô formula. Finally, an example is given to illustrate the theoretical results.
External DCR, EN-DCR, and TC-DCR had similar success and complication rates in patients with primary acquired nasolacrimal duct obstruction. External DCR resulted in the largest ostium size. Transcanalicular DCR appeared to be effective with the shortest surgical time.
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