Comments to Symmetrical Smoothing Method and First Step to How to Avoid Irrelevant Extremums

TL;DR

This paper analyzes the symmetrical smoothing method, identifies issues with extraneous solutions during optimization, and proposes a simple approach to avoid irrelevant extremums, improving the method's reliability.

Contribution

It introduces a straightforward technique to eliminate irrelevant extremums in the symmetrical smoothing method, enhancing its effectiveness in optimization tasks.

Findings

Identified causes of extraneous solutions in the smoothing method

Proposed a simple approach to avoid irrelevant extremums

Improved reliability of the symmetrical smoothing optimization process

Abstract

The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making optimization, besides symmetric solution, can occur another pretendents for the solution, which depends on $\sigma$. Next we show simple way how to avoid them.