A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts
Abstract
We develop an infeasible-start extension of the Topkis--Veinott feasible-direction method for nonconvex composite optimization. At each main iteration, a strongly convex local model is used to obtain objective descent while limiting increases in constraint violation. A separate feasibility-reduction step is invoked when feasibility improvement is needed. Under a feasibility-reduction condition, we establish the standard first-order rate for reducing the Fritz John residual and constraint violation. We then verify that both proximal-gradient and regularized Gauss--Newton methods applied to minimizing the squared constraint-violation function satisfy the required feasibility-reduction property under a Polyak--Łojasiewicz condition. Numerical experiments compare the reduction methods, including an experimental prox-linear variant, and compare the scalar-regularized and curvature-enhanced subproblem formulations.
Related
- A Feasible Direction Method with Active-Set Identification for Derivative-Free Optimization
- ProLand: A New Infeasible Manifold Optimization Method for LoRA Fine-Tuning
- Randomized and Oracle-Based Feasible Directions Methods for Nonsmooth Nonconvex Constrained Optimization
- An Infeasible Method with Feasibility Safeguard for Nonsmooth Composite Optimization Over Manifolds
- Convergence of a Randomized Newton Method in Nonconvex Optimization
BibTeX
@misc{li2026feasibledirectiontype,
title = {{A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts}},
author = {Danlin Li and Johannes Milz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38842},
eprint = {2610.38842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38842},
}
RIS
TY - UNPB
TI - A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts
AU - Danlin Li
AU - Johannes Milz
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38842
UR - https://arxiv.org/abs/2610.38842
AB - We develop an infeasible-start extension of the Topkis--Veinott feasible-direction method for nonconvex composite optimization. At each main iteration, a strongly convex local model is used to obtain objective descent while limiting increases in constraint violation. A separate feasibility-reduction step is invoked when feasibility improvement is needed. Under a feasibility-reduction condition, we establish the standard first-order rate for reducing the Fritz John residual and constraint violation. We then verify that both proximal-gradient and regularized Gauss--Newton methods applied to minimizing the squared constraint-violation function satisfy the required feasibility-reduction property under a Polyak--Łojasiewicz condition. Numerical experiments compare the reduction methods, including an experimental prox-linear variant, and compare the scalar-regularized and curvature-enhanced subproblem formulations.
ER -