First-order and second-order epsilon-directional derivatives of a marginal function in convex programming with linear inequality constraints (Q1825133)

\textit{J. B. Hiriart-Urruty} [SIAM J. Control Optimization 22, 381-404 (1984; Zbl 0557.90077)] gave formulas of the first-order and second-order \(\epsilon\)-directional derivatives of a marginal function for a convex programming problem with linear equality constraints, that is, the image of a function under a linear mapping. In this paper, we extend his results to a problem with linear inequality constraints. The formula of the first-order derivative is given with the help of a duality theorem. A lower estimate for the second-order \(\epsilon\)-directional derivative is given.