Complete solutions to a Class of 8th Order Polynomial Optimization Problems

TL;DR

This paper introduces a novel approach using canonical dual transformation to solve a specific class of 8th order polynomial optimization problems, providing a systematic way to find all extrema and solve related algebraic equations.

Contribution

It develops a new method based on sequential canonical dual transformation for solving 8th order polynomial optimization problems and related algebraic equations.

Findings

All extrema can be obtained using the proposed method

Optimality conditions identify global and local extrema

Applications demonstrated through examples

Abstract

This paper presents a new class of 8th order canonical polynomials in n-dimensional real space. Based on the sequential canonical dual transformation, all extrema are obtained. The method can be used to solve the associated 7th order nonlinear algebraic equations. Optimality conditions are provided to find both global minimizers and local extrema. Applications are illustrated by examples.