An Exact Penalty Approach for Equality Constrained Optimization over a Convex Set
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912361321857024 |
|---|---|
| author | Xiao, Nachuan Tang, Tianyun Wang, Shiwei Toh, Kim-Chuan |
| author_facet | Xiao, Nachuan Tang, Tianyun Wang, Shiwei Toh, Kim-Chuan |
| contents | In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set $\{x \in \mathcal{X}: c(x) = 0\}$, where $\mathcal{X}$ is a closed convex subset of $\mathbb{R}^n$. 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 $\mathcal{X}$ 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. 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 $\mathcal{X}$ and inherits their convergence properties to solve problems that take the form of (NCP). Preliminary numerical experiments illustrate the high efficiency of directly applying existing solvers for optimization over $\mathcal{X}$ to solve (NCP) through (CDP). These numerical results further demonstrate the practical potential of our proposed constraint dissolving approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Exact Penalty Approach for Equality Constrained Optimization over a Convex Set Xiao, Nachuan Tang, Tianyun Wang, Shiwei Toh, Kim-Chuan Optimization and Control In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set $\{x \in \mathcal{X}: c(x) = 0\}$, where $\mathcal{X}$ is a closed convex subset of $\mathbb{R}^n$. 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 $\mathcal{X}$ 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. 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 $\mathcal{X}$ and inherits their convergence properties to solve problems that take the form of (NCP). Preliminary numerical experiments illustrate the high efficiency of directly applying existing solvers for optimization over $\mathcal{X}$ to solve (NCP) through (CDP). These numerical results further demonstrate the practical potential of our proposed constraint dissolving approach. |
| title | An Exact Penalty Approach for Equality Constrained Optimization over a Convex Set |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.02495 |