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Bibliographic Details
Main Authors: Brilli, Andrea, Cristofari, Andrea, Liuzzi, Giampaolo, Lucidi, Stefano
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.10801
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Table of Contents:
  • In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for unconstrained and linearly constrained problems. In particular, when minimizing a function with $n$ variables, we prove that at most ${\cal O(nε^{-2})}$ iterations are needed to drive a criticality measure below a predefined threshold $ε$, requiring at most ${\cal O(n^2ε^{-2})}$ function evaluations. We also show that the total number of iterations where the criticality measure is not below $ε$ is upper bounded by ${\cal O(n^2ε^{-2})}$. Moreover, we investigate the method capability to identify active constraints at the final solutions. We show that, after a finite number of iterations, all the active constraints satisfying the strict complementarity condition are correctly identified.