Simple solution methods for separable mixed linear and quadratic knapsack problem

The Separable Convex Quadratic Knapsack Problem

This paper considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP is developed for solving this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The start...

Exact Solution Methods for the k-Item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 k-item quadratic knapsack problem (kQKP ), a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we st...

Exact Solution of the Quadratic Knapsack Problem

The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coeecients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We propose an exact branch-and-bound algorithm...

Reoptimization in lagrangian methods for the quadratic knapsack problem

A library for continuous convex separable quadratic knapsack problems

The Continuous Convex Separable Quadratic Knapsack problem (CQKnP) is an easy but useful model that has very many different applications. Although the problem can be solved quickly, it must typically be solved very many times within approaches to (much) more difficult models; hence an efficient solution approach is required. We present and discuss a small open-source library for its solution th...