Optimality Conditions and Constraint Qualifications for Mathematical Program with Geometric Constraints

数学学院学术报告

报告题目：Optimality Conditions and Constraint Qualifications for Mathematical Program with Geometric Constraints

报告时间：2017年7月10日（周一）下午16：00点-17:00点

报告地点：创新园大厦A1101

报告人：张进  香港浸会大学

校内报告联系人：刘永朝                                   联系电话：84708351-8141

报告摘要：

We study the mathematical program with geometric constraints (MPGC) such that the image of a mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the nonsmooth enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. In the case where the Banach space is a weakly compactly generated Asplund space, the optimality condition obtained can be expressed in terms of the limiting subdifferential while in the general case it can be expressed in terms of the Clarke subdifferential. One of the technical difficulties in obtaining such a result in an infinite dimensional space is that no compactness result can be used to show the existence of local minimizers of a perturbed problem. We employ the celebrated Ekeland's variational principle to obtain the results instead. The enhanced Fritz John condition allows us to obtain the enhanced Karush-Kuhn-Tucker condition under the pseudonormality and the quasinormality conditions which are weaker than the classical normality conditions. We then prove that the quasinomality is a sufficient condition for the existence of local error bounds of the constraint system. Finally we obtain a tighter upper estimate for the subdifferentials of the value function of the perturbed problem in terms of the enhanced multipliers.

报告人简介：张进，1986年3月出生，香港浸会大学研究助理教授。2007年于大连理工大学人文社会科学学院获文学学士，2010年于大连理工大学数学科学学院获得理学硕士学位，2014年12月于加拿大维多利亚大学数学与统计系获得应用数学博士学位。2015年7月进入香港浸会大学数学系工作。张进主要从事最优化理论方面，特别是最优性条件和约束规格方面的研究，发表SCI检索论文10余篇，其中有论文发表在 Mathematical Programming，SIAM Journal on Optimization等优化领域顶级期刊上。