Minimization of Quadratic Binary Functional with Additive Connection Matrix

TL;DR

This paper investigates quadratic binary functionals with additive connection matrices, deriving a formula for their global minimum and analyzing the complexity of their energy surfaces through simulations.

Contribution

It provides a method to find the global minimum of quadratic binary functionals with additive matrices using external parameters, advancing understanding of their energy landscapes.

Findings

Global minimum expressed via external parameters

Energy surface is complex and rugged

Simulations confirm theoretical complexity

Abstract

(NxN)-matrix is called additive when its elements are pair-wise sums of N real numbers. For a quadratic binary functional with an additive connection matrix we succeeded in finding the global minimum expressing it through external parameters of the problem. Computer simulations show that energy surface of a quadratic binary functional with an additive matrix is complicate enough.