报告题目：Second-Order Cone Reformulation Technique ofExtended Trust-Region Problems
摘 要：We consider the extended Celis-Dennis-Tapia (CDT)problem that has a positive duality gap. It is presented in theory that thispositive duality gap can be narrowed by adding an appropriate second-order-cone(SOC) constraint, which may lead to dividing the problem into two separatesubproblems. More concretely, for any extended CDT problem with a positive dualitygap, we prove that one SOC constraint is valid to narrow the positive dualitygap if and
only if the corresponding hyperplane intersects the openoptimal line segment. Especially when the second constraint function consistsof the product of two linear functions, we prove that the
positive duality gap can be eliminated thoroughly bysolving two subproblems with SOC constraints. For any classical CDT problemwith a positive duality gap, a new model with two SOC constraints
is proposed, and a sufficient condition is presentedunder which this positive duality gap can be eliminated thoroughly. Inparticular, based on the sufficient condition, it is proved that the positive
duality gaps of any two-dimensional classical CDTproblem and a class of three-dimensional classical CDT problems can beeliminated thoroughly. Numerical results of some gap-existing examples comingfrom other papers show that their positive duality gaps are indeed eliminatedby our SOC reformulation technique.
报告人简介：艾文宝，北京市教学名师，现任北京邮电大学数学系教授、博士生导师、数学系主任。主要研究方向为最优化理论与算法及其应用，在内点算法、非凸二次约束二次优化问题等领域取得了一系列重要的理论结果，这些结果发表在SIAM Optimation、Mathematical Programming等国际知名优化类顶尖学术期刊上。主持国家自然科学基金面上项目多项。目前是北京数学会理事、国际《数学评论》评论员，也是SIAM Optimation、MP等多个国际知名期刊的审稿人。