Efficiency and Convergence Insights in Large-Scale Optimization Using the Improved Inexact-Newton-Smart Algorithm and Interior-Point Framework

TL;DR

This paper compares the efficiency and convergence of the Improved Inexact-Newton-Smart algorithm with an interior-point framework for large-scale nonlinear optimization, highlighting their relative strengths and sensitivities.

Contribution

It provides a comprehensive evaluation of INS versus interior-point methods, revealing their performance differences and parameter sensitivities in large-scale optimization.

Findings

Interior-point method converges faster with fewer iterations.

INS benefits from regularization and step-length tuning.

Interior-point method shows stable performance across parameters.

Abstract

We present a head-to-head evaluation of the Improved Inexact--Newton--Smart (INS) algorithm against a primal--dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method converges with roughly one third fewer iterations and about one half the computation time relative to INS, while attaining marginally higher accuracy and meeting all primary stopping conditions. By contrast, INS succeeds in fewer cases under default settings but benefits markedly from moderate regularization and step-length control; in tuned regimes its iteration count and runtime decrease substantially, narrowing yet not closing the gap. A sensitivity study indicates that interior-point performance remains stable across parameter changes, whereas INS is more affected by step length and regularization choice. Collectively, the evidence positions the interior-point method as a reliable baseline and INS as a configurable alternative when problem structure favors adaptive regularization.