Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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,  strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method.  review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.
['Lucas Létocart', 'Angelika Wiegele']
I am writing a research paper on a idea Exact Solution Methods for the $k$-item Quadratic Knapsack Problem
[{"from": "human", "value": "I am writing a research paper on a idea Exact Solution Methods for the $k$-item Quadratic Knapsack Problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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,  strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method.  review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities."}]