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題目: A primal-dual majorization-minimization method for large-scale linear programs

報(bào)告人:戴彧虹研究員(中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院)

時(shí)間: 2023年9月28日上午10:30-11:30

地點(diǎn):數(shù)學(xué)學(xué)院425報(bào)告廳

邀請(qǐng)人:白敏茹

摘要: We present a primal-dual majorization-minimization method for large-scale linear programs. The method is originated from a newly developed augmented Lagrangian method for nonlinear inequalityconstrained optimization. The majorization-minimization approach is introduced to solve the augmented Lagrangian subproblems. Distinguished from the existing simplex methods and interior-point methods for linear programs, our proposed method only depends on a factorization of the constant matrix independent of iterations and does not need any computation on step sizes, thus can be expected to be particularly appropriate for large-scale linear programs. Under mild conditions, the global convergence is analyzed. Moreover, we prove that our method can be of globally linear convergence, and the iteration complexity of our method is independent of the sizes of the linear programs. This is a joint work with X.W.Liu and Y.K.Huang.

個(gè)人簡(jiǎn)介:

??戴彧虹研究員，現(xiàn)任中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院副院長(zhǎng)，亞太運(yùn)籌學(xué)會(huì)聯(lián)合會(huì)主席，中國(guó)運(yùn)籌學(xué)會(huì)理事長(zhǎng)。戴彧虹研究員長(zhǎng)期從事優(yōu)化方法的理論及應(yīng)用研究，在非線(xiàn)性?xún)?yōu)化、整數(shù)規(guī)劃與應(yīng)用優(yōu)化方面做出了系統(tǒng)和創(chuàng)造性的工作。他發(fā)展和完善了非線(xiàn)性共軛梯度法理論并提出Dai-Yuan方法；發(fā)展和完善了梯度法理論并提出Dai-Fletcher方法；提出最少約束違背優(yōu)化新方向并給出基礎(chǔ)理論與算法；獨(dú)立解決BFGS擬牛頓法收斂性公開(kāi)問(wèn)題以及合作解決一般升維覆蓋割計(jì)算復(fù)雜性公開(kāi)問(wèn)題；2018年和學(xué)生自主研發(fā)了國(guó)內(nèi)第一個(gè)現(xiàn)代意義上整數(shù)規(guī)劃求解器CMIP。方法和成果被優(yōu)化理論和應(yīng)用界大量引用。

??戴彧虹研究員曾應(yīng)邀在2022年國(guó)際數(shù)學(xué)家大會(huì)做45分鐘邀請(qǐng)報(bào)告，在2016年第五屆國(guó)際連續(xù)優(yōu)化會(huì)議（國(guó)際數(shù)學(xué)優(yōu)化學(xué)會(huì)旗艦會(huì)議）做半大會(huì)報(bào)告，在2022年第24屆國(guó)際數(shù)學(xué)規(guī)劃大會(huì)（國(guó)際數(shù)學(xué)優(yōu)化學(xué)會(huì)最大規(guī)模會(huì)議）作一小時(shí)大會(huì)報(bào)告。他曾獲國(guó)家自然科學(xué)二等獎(jiǎng)（完成人：袁亞湘 戴彧虹）、中國(guó)青年科技獎(jiǎng)、陳省身數(shù)學(xué)獎(jiǎng)、馮康科學(xué)計(jì)算獎(jiǎng)、首屆蕭樹(shù)鐵應(yīng)用數(shù)學(xué)獎(jiǎng)、國(guó)際通信大會(huì)最佳論文獎(jiǎng)。 2023年當(dāng)選國(guó)際運(yùn)籌學(xué)聯(lián)合會(huì)(IFORS)會(huì)士.