# An Alternative Globalization Strategy for Unconstrained Optimization

## TL;DR

This paper introduces a novel globalization strategy for unconstrained optimization that employs multiple points per iteration to enhance convergence speed and robustness, supported by theoretical guarantees and numerical experiments.

## Contribution

It presents a new multi-point based globalization approach for unconstrained optimization with proven convergence and practical parallel implementation.

## Key findings

- Supports rapid convergence from remote starting points
- Demonstrates promising numerical results
- Provides parallel implementation details

## Abstract

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a representative model of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy.