Level-constrained programming (Q1184818)

Let \(X\) be a real reflexive Banach space, which is strictly convex and smooth. Let \(F_ i: X\to\mathbb{R}\) be locally Lipschitz and regular. The problem: minimize \(F_ 0(x)\) s.t. \(F_ i(x)\leq 0\), \(i=1,\dots,m\), with the restriction \(F_ 0(x)\geq\mu\). This is an inequality constrained program. The last condition is meant to reflect tight bounds on the attained objective value. For example, in economic planning, the condition may signify that an enterprise should make no pure profit. The author develops an infinitesimal algorithm, without assumptions about strict feasibility, for this class of programs in which the optimal value is known a priori.