應(yīng)理學(xué)院邀請(qǐng)，國(guó)家優(yōu)秀青年基金獲得者、中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院劉歆副研究員將來(lái)我校進(jìn)行學(xué)術(shù)交流，并做學(xué)術(shù)報(bào)告。
報(bào)告時(shí)間：2016年9月22日周四上午10:00—11:00
報(bào)告地點(diǎn)：西教五416（理學(xué)院）
報(bào)告題目：A New First-order Framework for Orthogonal Constrained Optimization Problems
報(bào)告摘要：
In this talk, we consider a class of orthogonal constrained optimization problems, the feasible region of which is called the Stiefel manifold. Our new proposed framework combines a function value reduction stage with a multiplier symmetrization stage. Different with the existing approaches, the function value reduction is conducted in the Euclidean space instead of the Stiefel manifold or its tangent space. We construct two types of algorithms based on this new framework. The first type consists of gradient reflection (GR) and gradient projection (GP). The other one adopts a column-wise block coordinate descent (CBCD) scheme. A novel idea is developed for solving the corresponding CBCD subproblem inexactly. Theoretically, we can prove that both of GR/GP with fixed stepsize and CBCD belong to our framework, and any clustering point of the iterates generated by the proposed framework is a first-order stationary point. The iterate convergence and local convergence rate of the new framework can be established in some special cases. We compare our new framework with the state-of-the-art solvers in solving a class of quadratic problems, and also compare our GR algorithm with those default solvers in KSSOLV in solving a few typical KS energy minimization problems. Preliminary experiments illustrate that our new framework is of great potential.
報(bào)告人簡(jiǎn)介：
劉歆，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院副研究員，2016年國(guó)家優(yōu)秀青年科學(xué)基金獲得者。2004年本科畢業(yè)于北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院。2009年于中國(guó)科學(xué)院研究生院(現(xiàn)中國(guó)科學(xué)院大學(xué))獲理學(xué)博士學(xué)位，導(dǎo)師袁亞湘院士。2009年至2010年于德國(guó)ZIB研究所做博士后，2010年至2011年在美國(guó)RICE大學(xué)計(jì)算與應(yīng)用數(shù)學(xué)系訪(fǎng)問(wèn)，2014年入選中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院“陳景潤(rùn)未來(lái)之星”計(jì)劃。現(xiàn)為國(guó)際期刊《Mathematical Programming Computation》編委。
劉歆主要從事最優(yōu)化計(jì)算方法的研究工作，主持并完成一項(xiàng)國(guó)家自然科學(xué)基金青年基金項(xiàng)目，現(xiàn)主持一項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目；此外還參與國(guó)家自然科學(xué)基金委重大研究計(jì)劃、重點(diǎn)項(xiàng)目、國(guó)際交流合作項(xiàng)目以及科技部863項(xiàng)目等。具體的研究方向包括：非線(xiàn)性最小二乘問(wèn)題、矩陣低秩分解理論及其算法、非線(xiàn)性特征值問(wèn)題、分布式優(yōu)化算法等。
