Exact Solution Procedure for the Log-Linear Continuous Knapsack Problem

TL;DR

This paper introduces an exact algorithm for solving the log-linear continuous knapsack problem, leveraging duality and slackness theorems to handle the concave objective function efficiently.

Contribution

The paper presents a novel exact solution procedure specifically designed for the log-linear continuous knapsack problem, expanding the toolkit for such nonlinear optimization challenges.

Findings

Algorithm guarantees exact solutions for the problem.

Utilizes duality and slackness theorems for efficiency.

Applicable to a class of concave optimization problems.

Abstract

We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear optimization problem with linear objective function that is associated with any solution of a linear optimization problem with (differentiable) concave objective function.