應(yīng)yl7703永利官網(wǎng)李朋副教授邀請(qǐng), 中山大學(xué)數(shù)據(jù)科學(xué)與計(jì)算 機(jī)學(xué)院李洽副教授, 將于2022年11月3號(hào)(星期四)上午10:00在線舉辦學(xué)術(shù)報(bào)告.

報(bào)告題目：First-orderAlgorithms forAClass ofFractionalOptimizationProblems

騰訊會(huì)議ID:609-555-634

報(bào)告摘要:We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator is a nonsmooth convex function. In this work, we first derive its first-order necessary optimality condition, by using the first-order operators of the three functions involved. Then we develop first-order algorithms, namely, the proximity-gradient-subgradient algorithm (PGSA),PGSA with monotone line search (PGSA-ML) and PGSA with nonmonotone line search (PGSA-NL). It is shown that any accumulation point of the sequence generated by them is a critical point of the problem under mild assumptions. Moreover, we establish global convergence of the sequence generated by PGSA or PGSA-ML and analyze its convergence rate, by further assuming the local Lipschitz continuity of the nonsmooth function in the numerator, the smoothness of the denominator and the Kurdyka-Lojasiewicz (KL) property of the objective. The proposed algorithms are applied to the sparse generalized eigenvalue problem associated with a pair of symmetric positive semidefinite matrices and the corresponding convergence results are obtained according to their general convergence theorems. We perform some preliminary numerical experiments to demonstrate the efficiency of the proposed algorithms.

報(bào)告人簡(jiǎn)介

李洽, 中山大學(xué)數(shù)據(jù)科學(xué)與計(jì)算機(jī)學(xué)院副教授、博士生導(dǎo)師. 2013年獲中山大學(xué)數(shù)學(xué)(信息計(jì)算科學(xué)方向)博士學(xué)位；博士期間曾赴美國(guó)Syracuse University數(shù)學(xué)系訪問(wèn)一年；現(xiàn)任中山大學(xué)計(jì)算機(jī)學(xué)院科學(xué)計(jì)算系副主任, 廣東省計(jì)算數(shù)學(xué)學(xué)會(huì)理事. 研究領(lǐng)域包括最優(yōu)化理論、算法及在機(jī)器學(xué)習(xí)、數(shù)據(jù)分析與圖像處理等領(lǐng)域的應(yīng)用, 相關(guān)論文在ACHA、SIOPT、IP、TMI等應(yīng)用與計(jì)算數(shù)學(xué)知名期刊上發(fā)表, 其中一篇獲評(píng)Inverse Problems期刊2017年度Highlights. 主持項(xiàng)目包括國(guó)家自然科學(xué)基金兩項(xiàng)(青年基金與面上項(xiàng)目)以及廣東省自然科學(xué)基金, 參與項(xiàng)目包括國(guó)家重大研究計(jì)劃集成項(xiàng)目、廣東省重點(diǎn)研發(fā)計(jì)劃.詳情請(qǐng)見(jiàn)李洽教授個(gè)人主頁(yè)：https://cse.sysu.edu.cn/content/2566

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2022年10月28日