**Boltz** 's problem is a problem of the theory of optimal control of the form:

- $\dot{x}(t)=f(t,x(t),u(t)),{t}_{0}\le t\le T,x({t}_{0})={x}_{0}$
- $J(u)=\underset{{t}_{0}}{\overset{T}{\int}}F(t,x(t),u(t))dt+\phi (x({t}_{0}),x(T))\to inf$ ,

in which you want to minimize functionality$J(u)$ mixed type. The problem easily reduces to the Mayer problem , which allows us to use the theorem on the necessary optimality conditions to solve the problem.

Formulated in 1913 by Oscar Bolzey .

## Links

*Bolza's challenge*- an article from the Mathematical Encyclopedia . I. B. Vapnyarsky