2025年09月06日 星期六 登录 EN

学术活动
Partial Envelope for Constrained Optimization with Constraints
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报告人:
Nachuan Xiao, Assistant Professor, The Chinese University of Hong Kong, Shenzhen
邀请人:
Xin Liu, Professor
题目:
Partial Envelope for Constrained Optimization with Constraints
时间地点:
10:00-11:00 September 8(Monday), Tencent Meeting: 180110846, Password: 311311
摘要:

In this talk, 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 $\mathbb{R}^n$. Building upon the forward-backward envelope framework for optimization over $\mathcal{X}$, we propose a novel forward-backward semi-envelope (FBSE) approach for solving (NCP). In the proposed FBSE approach, we eliminates the constraint $x \in \mathcal{X}$ through a specifically designed envelope scheme while preserving the constraint $x \in \mathcal{M} := \{x \in \mathbb{R}^n: c(x) = 0\}$. We establish that the FBSE for (NCP) is well-defined and locally Lipschitz smooth over a neighborhood of $\mathcal{M}$. Furthermore, we prove that (NCP) and its corresponding FBSE have same first-order stationary points within a neighborhood of $\mathcal{X}$. Consequently, our proposed FBSE approach enables direct application of optimization methods over $\mathcal{M}$ while inheriting their convergence properties for problems of the form (NCP). Additionally, we develop an inexact projected gradient descent method for minimizing the forward-backward semi-envelope over $\mathcal{M}$ and establish its global convergence. Preliminary numerical experiments demonstrate the practical efficacy and potential of our proposed approach.