Efficient Algorithms for a Convex Programming Problem with a Constraint on the Weighted Total Amount

摘要

This paper investigates a king of resource allocation problems which maximizes an objective function of being strictly concave with a constraints on the weighted total amount of resources. It is thought to be a convex minimization problem. We derive necessary and sufficient conditions for optimality and propose two methods For solving the problem, which manipulate so-called lagrange multiplier so as to finally Satisfy the conditions.