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“創(chuàng)源”大講堂研究生學(xué)術(shù)講座

海 報(bào)

講座時(shí)間： 2022年12月9日14:30—15:30

講座地點(diǎn)：騰訊會(huì)議號(hào)：393 812 857；密碼：1209

主講人簡(jiǎn)介：

夏福全，四川師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士研究生導(dǎo)師。主要從事最優(yōu)化理論及應(yīng)用方面的研究。到現(xiàn)在為止，已在國(guó)內(nèi)外知名學(xué)術(shù)刊物上發(fā)表SCI收錄論文30余篇，主持了四川省教育廳基金，四川省科技廳應(yīng)用基礎(chǔ)項(xiàng)目，教育部博士點(diǎn)基金和教育部重點(diǎn)項(xiàng)目。應(yīng)邀多次訪問了臺(tái)灣的國(guó)立中山大學(xué)、高雄醫(yī)學(xué)大學(xué)和長(zhǎng)庚大學(xué)，韓國(guó)的Gyeongsang大學(xué)和Gyungnam大學(xué)。

講座內(nèi)容簡(jiǎn)介：

Title: Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems

(Joint work with Zhichun Yang, Kai Tu and Man-Chung Yue)

Abstract. We consider the problem of minimizing a large sum of smooth convex functions subject to a large number of constraints defined by convex functions that are possibly non-smooth. Such a problem finds a wide range of applications in many areas, such as machine learning and signal processing. In this paper, we devise a new random projection method (RPM) for efficiently solving this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projection onto a subset of the feasible region, our algorithm requires only a relaxed projection in the sense that only the projection onto a half-space approximation of the subset is needed. This significantly reduces the per iteration computational cost as the relaxed projection admits a closed-form formula. Second, to exploit the structure that the objective function is a large sum of convex functions, the variance reduction technique is incorporated into our algorithm to improve the empirical convergence behaviour. As our theoretical contributions, under an error bound-type condition and some other standard conditions, we prove that almost surely the proposed algorithm converges to an optimal solution and that both the optimality and feasibility gaps decrease to zero, with rates and , respectively. As a side contribution, we also show that the said error bound-type condition holds some mild assumptions, which could be of independent interest. Numerical results on synthetic problem instances are also presented to demonstrate the practical effectiveness of the variance reduction technique and the superiority of our proposed RPM as compared with two existing ones.