Affiliation:
1. Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260;
2. Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Abstract
Interior point methods (IPMs) that handle nonconvex constraints such as IPOPT, KNITRO and LOQO have had enormous practical success. We consider IPMs in the setting where the objective and constraints are thrice differentiable, and have Lipschitz first and second derivatives on the feasible region. We provide an IPM that, starting from a strictly feasible point, finds a μ-approximate Fritz John point by solving [Formula: see text] trust-region subproblems. For IPMs that handle nonlinear constraints, this result represents the first iteration bound with a polynomial dependence on [Formula: see text]. We also show how to use our method to find scaled-KKT points starting from an infeasible solution and improve on existing complexity bounds. Funding: This work was supported by Air Force Office of Scientific Research [9550-23-1-0242]. A significant portion of this work was done at Stanford where O. Hinder was supported by the PACCAR, Inc., Stanford Graduate Fellowship and the Dantzig-Lieberman fellowship.
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Subject
Management Science and Operations Research,Computer Science Applications,General Mathematics