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

Neda Bagheri Renani (), Maryam Jaefarzadeh and Daniel Ševčovič
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Neda Bagheri Renani: Department of Applied Mathematics and Statistics, Comenius University in Bratislava, Mlynská Dolina, 84248 Bratislava, Slovakia
Maryam Jaefarzadeh: Department of Mathematical and Computer Science, Sheikhbahaee University, Isfahan 81799-41996, Iran
Daniel Ševčovič: Department of Applied Mathematics and Statistics, Comenius University in Bratislava, Mlynská Dolina, 84248 Bratislava, Slovakia

Mathematics, 2025, vol. 13, issue 22, 1-15

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.

Keywords: nonlinear optimization; interior-point; Newton-type algorithms; large-scale optimization; convergence; performance; Hessian regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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