AN O(N(3)LOG N) STRONG POLYNOMIAL ALGORITHM FOR AN ISOTONIC REGRESSION KNAPSACK-PROBLEM

We introduce the isotonic regression knapsack problem [GRAPHICS] where each di is positive and each alpha(i), a(i), i = 1,...,n, and c are arbitrary scalars. This problem is the natural extension of the isotonic regression problem which permits a strong polynomial solution algorithm. In this paper, an approach is developed from the Karush-Kuhn-Tucker conditions. By considering the Lagrange function without the inequalities, we establish a way to find the proper Lagrange multiplier associated with the equation using a parametric program, which yields optimality. We show that such a procedure can be performed in strong polynomial time, and an example is demonstrated.