Optimization of Quadratic Forms: NP Hard Problems : Neural Networks

TL;DR

This paper investigates the NP-hard problem of optimizing quadratic forms over hypercube convex hulls, exploring stable states and their computation, with implications for the P vs NP question.

Contribution

It presents new insights into the NP-hard quadratic optimization problem over hypercube convex hulls and discusses stable states and global optima.

Findings

Results on stable and anti-stable states over the hypercube

Discussion on computing global optimum stable states

Implications for the P vs NP problem

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. Some results related to stable states/vectors, anti-stable states/vectors (over the hypercube) are discussed. Some results related to the computation of global optimum stable state (an NP hard problem) are discussed. It is hoped that the results shed light on resolving the P \neq NP problem.