ICCOPT2025USC

Session: Parametric Optimization Problems
Chair: Xiaoqi Yang
Cluster: Fixed Points and Variational Inequalities

Talk 1: Recent stability results in parametric optimization
Speaker: Xiaoqi Yang
Abstract: Recover bounds/relative calmness for sparse optimization models are important for algorithmic convergence analysis in machine learning and compressed sensing. Some recent results in sparse optimization obtained by restricted isometry property and restricted eigenvalue conditions will be reviewed. Lipschitz-like property and Lipschitz continuity are at the core of stability analysis. A projectional coderivative of set-valued mappings will be discussed and and be applied to obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set.

Talk 2: Lipschitz continuity of solution multifunctions of extended l_1 regularization problems
Speaker: Kaiwen Meng
Abstract: In this paper we obtain a verifiable sufficient condition for a polyhedral multifunction to be Lipschitz continuous on its domain. We apply this sufficient condition to establish the Lipschitz continuity of the solution multifunction for an extended l_1 regularization problem with respect to the regularization parameter and the observation parameter under the assumption that the data matrix is of full row rank.

Talk 3: Existence of a solution for stochastic multistage vector variational inequality problems
Speaker: Shengkun Zhu
Abstract: In this talk, we will discuss basic form and extensive forms of a stochastic vector variational inequality problem. We will apply KKM theorem to prove the existence of a solution under the monotonicity and hemi-continuity assumptions.