In this paper, we consider the nonlinear constrained optimization problem (NCP) with a constraint set 1C := {x is an element of X : c(x) = 0}, where X is a closed convex subset of Rn. We propose an exact penalty approach, named constraint dissolving approach, that transforms (NCP) into its corresponding constraint dissolving problem (CDP). The transformed problem (CDP) admits X as its feasible region with a locally Lipschitz smooth objective function. We prove that (NCP) and (CDP) share the same first-order stationary points, second-order stationary points, second-order sufficient condition (SOSC) points, and strong SOSC points, in a neighborhood of the feasible region 1C. Moreover, we prove that these equivalences extend globally under a particular error bound condition. Therefore, our proposed constraint dissolving approach enables direct implementations of optimization approaches over X and inherits their convergence properties for solving problems of the form (NCP). Preliminary numerical experiments illustrate the high efficiency of directly applying existing solvers for optimization over X to solve (NCP) through (CDP). These numerical results further demonstrate the practical potential of our proposed constraint dissolving approach.

Publication:

MATHEMATICAL PROGRAMMING

https://doi.org/10.1007/s10107-026-02367-9

Author:

Xiao, Nachuan

Chinese Univ Hong Kong, Sch Data Sci, Shenzhen, Peoples R China

Email address: xnc@lsec.cc.ac.cn

Tang, Tianyun

Univ Chicago, Dept Stat, Chicago, IL USA

Email address: ttang@u.nus.edu

Wang, Shiwei(corresponding author)

Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci AMSS, Beijing, Peoples R China

Natl Univ Singapore, Inst Operat Res & Analyt, Clementi, Singapore, Singapore

Email address: wangshiwei@amss.ac.cn

Toh, Kim-Chuan

Natl Univ Singapore, Dept Math, Clementi, Singapore, Singapore

Email address:mattohkc@nus.edu.sg