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 a rbitrary scalars. This problem is the natural extension of the isotoni c regression problem which permits a strong polynomial solution algori thm. In this paper, an approach is developed from the Karush-Kuhn-Tuck er conditions. By considering the Lagrange function without the inequa lities, we establish a way to find the proper Lagrange multiplier asso ciated with the equation using a parametric program, which yields opti mality. We show that such a procedure can be performed in strong polyn omial time, and an example is demonstrated.