报告时间：2021年4月23日上午9:00-10:30

报告地点：数计院会议室（玉衡北302）

报告题目：Equipping the Barzilai-Borwein gradient method with two-dimensional quadratic termination property

报告人：中国科学院数学与系统科学研究院戴彧虹研究员

邀请人：童小娇

报告人简介：戴彧虹，中国科学院数学与系统科学研究院研究员，博士生导师。他主要研究连续优化、整数规划以及应用优化，已发表论文一百三十余篇，出版专著一本。曾获国家自然科学二等奖（排名第二）、第十届中国青年科技奖、国家杰出青年科学基金、第十一届冯康科学计算奖、第十六届陈省身数学奖和首届萧树铁应用数学奖。曾访问英国剑桥大学、邓迪大学、德国拜罗伊特大学、美国康奈尔大学等院校。目前担任中国运筹学会理事长、中科院数学与系统科学研究院优化与应用研究中心主任。担任《International Transactions in Operational Research》、《Science China Mathematics》、《Journal of Global Optimization》、《COAP》等杂志编委。曾主持国家杰出青年科学基金、中国科学院科技创新“交叉与合作团队”项目、国家自然科学基金重点项目以及创新研究群体项目等基金与项目。

报告摘要：Sinceits proposition in Cauchy (1847), one milestone work along the gradient method is the Barzilai-Borwein (nonmonotone) method (1988), while another significant work is the Yuan stepsize in (2006), which leads to the appearance of the efficient Dai-Yuan (monotone) gradient method (2005). In this talk, a new gradient stepsize will be delivered at the motivation of equiping the Barzilai-Borwein method with two-dimensional quadratic termination property. A remarkable feature of the new stepsize is that its computation only depends on the Barzilai-Borwein stepsizes in two previous iterations, without the need for exact line searches and Hessian, and hence it can easily be extended for nonlinear optimization. By adaptively taking long Barzilai-Borwein steps and some short steps associated with the new stepsize, we develop an efficient gradient method for unconstrained optimization. The proposed method is further extended for box-constrained constrained optimization and singly linearly box-constrained optimization by incorporating nonmonotone line searches and gradient projection techniques. Numerical experiments demonstrate that the proposed method outperforms the most successful gradient methods in the literature. This is a joint work with Yakui Huang and Xinwei Liu.