Complexity results and active-set identification of a derivative-free method for bound-constrained problems
Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: Sapienza University of Rome, University of Rome Tor Vergata
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391948463