Leap Gradient Algorithm

TL;DR

The paper introduces the Leap Gradient Algorithm, a novel method for global univariate optimization that does not require convexity and efficiently finds global extrema of real analytic functions.

Contribution

It presents a new algorithm that combines evolutionary leaps with standard descent methods, enabling efficient global optimization without convexity assumptions.

Findings

Successfully finds global extrema of univariate real analytic functions.

Operates effectively without convexity of the target function.

Provides an efficient numerical method for global optimization.

Abstract

The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several evolutionary leaps the algorithm naturally becomes the standard descent (or ascent) procedure near the global extremum. Moreover, it leads us to an efficient numerical method for calculating the global extrema of univariate real analytic functions.