Coincidence of typical singularities of solutions of extremal problems with constraints (Q2771541)

This paper deals with the extremal problem \(f(x,q)\to\min\), \(G(x,q)=0,\) which is called problem with implicit constraint, and with the problem \(f(x)\to\min,\;g(x)=q\), which is called problem with explicit constraint. Here \(q\) is a parameter. One of the main results of this paper is a comparison of classification of typical singularities of the conditional minimum in the case of explicit and implicit constraints. The classification of typical singularities of the conditional minimum is found for the explicit constraint when the dimension of the parameter space is \(m<5\). Let \(n\) be a state space dimension. The authors prove that for \(m=4\) no new typical point singularities appear for \(n\geq 6\).NEWLINENEWLINEFor the entire collection see [Zbl 0949.00042].