Convex-valued Lipschitz differential inclusion and Pontryagin's maximum principle (Q2777857)

Let \(Q\) be a bounded open set in \(R^{m}\) and let \(F: R^{m}\to R^{m}\) be a convex-valued mapping. The author considers the problem \(J(p)\to\min\), \(\varphi(p)\leq 0\), \(g(p)=0\); \(\dot x\in F(x)\); \(x\in\text{cl} Q\), where \(p=(x(0); x(T))\in (\text{cl} Q)^2\); \(J,\varphi,g\) are Lipschitz functions on \((\text{cl} Q)^2\); \(J\) is a scalar function; \(\varphi,g\) are vector-valued functions. The necessary conditions for an extremum are obtained. These conditions are stronger than Clarke's maximum principle and are obtained from the classical Pontryagin's maximum principle.NEWLINENEWLINEFor the entire collection see [Zbl 0949.00043].