Optimization on
the intersection of manifolds:
orthogonal tangent directions
and geometric methods
报告专家：袁亚湘 研究员（中国科学院数学与系统科学研究院）
报告时间：5月17日（周日）14:00-15:00
报告地点：国家天元数学西南中心516
报告摘要：
Optimization problems constrained by the intersection of two manifolds have found broad applications in various fields. However, the coupling regions pose challenges for the development of efficient algorithms. To this end, we exploit the geometry of the manifold intersection to propose an infeasible method employing a retraction-based update based on two orthogonal directions, both of which are tangent to one of the manifolds. Specifically, the two directions are responsible for approaching the feasible intersection and minimizing the objective function, respectively. Under the assumption of intrinsic transversality, we prove an O(1/K) convergence rate for both the feasibility and the optimality measures. Numerical experiments on spherical data fitting, hyperbolic embedding approximation, and compressed modes confirm the efficiency of the proposed method.
Joint work with B. Gao and Y. Yang
专家简介：
袁亚湘，中国科学院数学与系统科学研究院研究员。中国科学院院士、发展中国家科学院院士、巴西科学院通讯院士、美国数学会首届会士、美国工业与应用数学学会会士、国际运筹学联合会会士、伦敦数学会荣誉会员。现任全国政协常委、中国科协副主席。曾任中国数学会理事长、中国运筹学会理事长、国际工业与应用数学联合会主席、国际运筹学联合会副主席。袁亚湘长期从事计算数学、应用数学、运筹学等领域研究工作并取得了系统成果，在信赖域法、拟牛顿法、非线性共轭梯度法、子空间方法等方面做出了重要贡献。他曾获FOX奖、首届冯康科学计算奖、中国数学会陈省身奖、华罗庚奖、中国工业与应用数学学会苏步青奖、美国工业与应用数学学会杰出贡献奖、国家自然科学二等奖等。
邀请人：连增
