A dual differentiable exact penalty function in fractional programming (Q1104869)

A dual differentiable penalty functiod. It is shown that under some assumptions the upper and lower directional derivatives of the value functions of such differential games satisfy certain relationships. At points of differentiability of the value functions these relationships reduce to the Isaacs equation. As it was shown earlier these relationships imply that the value is a viscosity solution of the Isaacs equation.