Consider a min–max problem in the form of minx∈X max1≤i≤m {fi(x)}. It is well-known that the non-differentiability of the max function F(x) ≡ max1≤i≤m {fi(x)} presents difficulty in finding an optimal solution. An entropic regularization procedure provides a smooth approximation Fp(x) that uniformly converges to F(x) over X with a difference bounded by ln(m)/p, for p > 0. In this way, with p being sufficiently large, minimizing the smooth function Fp(X) over X provides a very accurate solution to the min–max problem. The same procedure can be applied to solve systems of inequalities, linear programming problems, and constrained min–max problems.
