Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems. In this paper, we introduce an abstract but reasonable version of the prominent linear independence constraint qualification which applies to MPDCs. Afterwards, we derive first- and second-order optimality conditions for MPDCs under validity of this constraint qualification based on so-called strongly stationary points. Finally, we apply our findings to some popular classes of disjunctive programs and compare the obtained results to those ones available in the literature. Particularly, new second-order optimality conditions for mathematical programs with switching constraints are by-products of our approach.
Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints
Sufficient Conditions for Metric Subregularity of Constraint Systems with Applications to Disjunctive and Ortho-Disjunctive Programs
本文研究一般最优化问题的度量次正则约束规格（MSCQ），重点是非凸设置。我们详细阐述了方向伪正态性和准正态性的概念，最近由Bai等人（SIAM J. Opt.，2019年），它结合了标准的方法，通过伪和准常态与现代工具的方向变分分析。我们专注于应用程序的析取程序，其中（方向）伪正规性的特点是通过一个极值条件。这反过来又产生了有效的工具来验证伪正规性和MSCQ，其中包括但不限于Robinson关于多面体多函数的结果和Gfrerer关于度量次正则性的二阶充分条件。最后，我们完善我们的研究，通过定义一类新的ortho-disjunctive程序，其中包括突出的最优化问题，如数学规划的互补性，消失或切换约束。
On Constraint Qualifications for MPECs with Applications to Bilevel Hyperparameter Optimization for Machine Learning
School of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）；Beijing Key Laboratory on MCAACI/Key Laboratory of Mathematical Theory and Computation in Information Security, Beijing Institute of Technology（北京信息计算安全数学理论与计算重点实验室）；School of Mathematical Sciences, University of Southampton（南安普顿大学数学科学学院）
Feasible-Set Reshaping for Constraint Qualification in Optimization-Based Control
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University（合成过程工业综合自动化国家重点实验室，东北大学）；Tongji University（同济大学）；New York University（纽约大学）
Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
Department of Information System, Arizona State University（亚利桑那州立大学信息系统系）；Department of Business Analytics, University of Iowa（爱荷华大学商业分析系）；Department of Mathematical Sciences, Rensselaer Polytechnic Institute（伦塞拉尔_polytechnic学院数学科学系）
