A single-loop stochastic feasible interior-point algorithm for nonlinear inequality-constrained optimization
Year: 2026
Type: article
Abstract: An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and inequality constraint functions may be nonlinear and/or nonconvex, and when constraint values and derivatives are tractable to compute, but objective function values and derivatives can only be estimated. The algorithm is intended primarily for a setting that is similar for stochastic-gradient methods for unconstrained optimization, i.e., the setting when stochastic-gradient estimates are available and employed in place of gradients, and when no objective function values (nor estimates of them) are employed. This is achieved by the interior-point framework having a single-loop structure rather than the nested-loop structure that is typical of contemporary interior-point methods. Convergence guarantees for the framework are provided both for deterministic and stochastic settings. Numerical experiments show that the algorithm yields good performance on a large set of test problems.
Source: Mathematical Programming
Authors: Frank E. Curtis, Xin Jiang, Qi Wang
Institution: Lehigh University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7118288502