Towards a Resolution of P = NP Conjecture

TL;DR

This paper investigates the quadratic optimization problem over hypercube corners, proposing an algorithm and discussing implications for the P vs NP conjecture, aiming to shed light on one of the most fundamental questions in computer science.

Contribution

It introduces a new approach to quadratic form optimization over hypercube corners and proposes an algorithm that may contribute to resolving the P vs NP problem.

Findings

Optimal solutions occur at hypercube corners under certain conditions

Proposed algorithm for finding global optima in NP-hard problems

Discussion on implications for the P vs NP conjecture

Abstract

In this research paper, the problem of optimization of a quadratic form over the convex hull generated by the corners of hypercube is attempted and solved. It is reasoned that under some conditions, the optimum occurs at the corners of hypercube. Results related to the computation of global optimum stable state (an NP hard problem) are discussed. An algorithm is proposed. It is hoped that the results shed light on resolving the P not equal to NP problem.