An efficient computational procedure for solving entropy optimization problems with infinitely many linear constraints (Q1923627)

One considers the entropy optimization problem with an infinite number of linear constraints \[ \inf \sum^n_{j=1} x_j\ln x_j \text \;{ s.t. } \sum^n_{j=1} g_j(t)x_j\geq h(t),\;t\in T, \] where \(T\) is a compact metric space and \(g_1,\dots,g_n\) and \(h\) are real-valued continuous functions on \(T\). A cutting-plane type algorithm for solving the entropy optimization with an infinite number of linear constraints is proposed. In each iteration one solves a finite entropy optimization problem and adds one more constraint if an optimal solution is not identified. Under a mild condition the algorithm converges. Preliminary computational experience confirms the efficiency of the proposed method.