一、報告題目：求解線性方程組和不等式組的隨機算法
報告人簡介：
韓德仁，教授，博士生導師，現(xiàn)任北京航空航天大學數(shù)學科學學院院長。從事大規(guī)模優(yōu)化問題、變分不等式問題的數(shù)值方法的研究工作，以及優(yōu)化和變分不等式問題在交通規(guī)劃、磁共振成像中的應(yīng)用，發(fā)表多篇學術(shù)論文。曾獲中國運籌學會青年科技獎，江蘇省科學技術(shù)獎等獎項；主持國家自然科學基金杰出青年基金等多項項目。擔任中國運籌學會常務(wù)理事、算法軟件與應(yīng)用分會理事長；《數(shù)值計算與計算機應(yīng)用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》編委。
報告內(nèi)容簡介：
本報告介紹求解相容和不相容線性方程組和不等式組問題的隨機算法的幾個新進展，包括多集合Douglas-Rachford分裂算法（r-sets-DR (RrDR)）等。
二、報告題目：模型驅(qū)動與數(shù)據(jù)驅(qū)動的優(yōu)化反演問題及智能計算
報告人簡介：
王彥飛，研究員，從事反問題理論及正則化方法、反問題的數(shù)學優(yōu)化算法、計算及勘探地球物理、地學大數(shù)據(jù)與人工智能分析研究工作。主持國家重點研發(fā)計劃、基金重大計劃項目等多項，發(fā)表論文150余篇，出版學術(shù)論著6部，授權(quán)發(fā)明專利30余項。任中國科學院油氣資源研究重點實驗室主任、地球科學大數(shù)據(jù)與人工智能中心主任、大數(shù)據(jù)分析與人工智能地球物理學科組組長。入選多個國家高層次人才計劃。任中國運籌學會及數(shù)學智能分會常務(wù)理事、CSIAM反問題與成像專委會副主任。獲中國青年科技獎、國務(wù)院政府特殊津貼專家等多項榮譽。
報告內(nèi)容簡介：
In the field of geophysics, big data, AI, and inverse problems involve cross-disciplinary integration of computer science, mathematics, statistics, and geophysics. This approach enables the development of accurate subsurface property models by analyzing vast amounts of geophysical data. Traditionally, various geophysical methods were used to study geological anomalies, but the use of big data and AI has shown potential to enhance this process. This talk will introduce both model-driven and data-driven inverse problems and explain how optimizing algorithms are used to solve for physical properties of the earth’s subsurface from geophysical data collected at the surface.
三、報告題目：Regularized splitting method for three operators inclusion problems of “two maximal monotone + one cocoercive” and its applications
報告人簡介：
蔡邢菊，南京師范大學教授，博士生導師。主要從事最優(yōu)化理論與算法、變分不等式、數(shù)值優(yōu)化方向研究工作。主持多項國家基金，獲江蘇省科技進步獎一等獎一項，發(fā)表SCI論文50余篇。擔任中國運籌學會副秘書長、算法軟件與應(yīng)用分會秘書長、數(shù)學規(guī)劃分會常務(wù)理事，江蘇省運籌學會理事長。
報告內(nèi)容簡介：
Thisstudyconsiders finding a zero point of A + B + C, where A and C are maximal monotone and B is ξ-cocoercive. The three-operator splitting method (TSM), proposed by Davis and Yin, is a popular algorithm for solving this problem. Observing that the x-sequence and the y-sequence in TSM have the same accumulation point and B’s information is only utilized in the second subproblem, this work proposes a new splitting method named the regularized splitting method (RSM), where “x = y” is introduced as a penalty term and the forward step is also employed in the first subproblem. The penalty term can balance the differences between the two subproblems and the additional forward step enables utilizing B’s information in both subproblems simultaneously. We establish the convergence of the proposed method and demonstrate its sublinear convergence rate concerning the fixed-point residuals, assuming mild conditions in an infinite dimensional Hilbert space. This approach not only generalizes the Douglas-Rachford splitting method and the TSM, but also, to our knowledge, uniquely correlates with the symmetric alternating direction method of multipliers–a correspondence that is absent in current maximal monotone operator splitting algorithms. As an application, we use RSM to solve zero point problems involving multiple operators. By introducing a new space reconstruction method, we transform the problem of multiple operators into a problem of three operators and derive a distributed version of the RSM. We validate our method’s efficiency through applications to mean-variance optimization, inverse problems in imaging, and the softmargin support vector machine problem with nonsmooth hinge loss functions, showcasing its superior performance compared to existing algorithms in the literature.
四、報告題目：Simulated annealing-based nonmonotone conjugate gradient method for unconstrained optimization with applications
報告人簡介：
彭拯，湘潭大學數(shù)學與計算科學學院教授，博士生導師。主要從事數(shù)學優(yōu)化理論、算法及其應(yīng)用研究，當前研究興趣在于流形優(yōu)化與流形學習，以及超大規(guī)模集成電路物理設(shè)計、下一代通信網(wǎng)絡(luò)、新能源電力系統(tǒng)等理論與實際應(yīng)用中的大規(guī)模非凸非光滑優(yōu)化問題的求解算法，尤其關(guān)注隨機優(yōu)化算法與非單調(diào)優(yōu)化算法相關(guān)研究。主持國家重要科研項目6項，省部級項目5項。當前兼任中國運籌學會理事、湖南省運籌學會副理事長，中國運籌學會算法軟件及其應(yīng)用分會常務(wù)理事和數(shù)學規(guī)劃分會理事。
報告內(nèi)容簡介：
Line search methods typically require a large number of iterations to find the suitable stepsize, resulting in slower convergence speed and higher computation cost. Combining with nonmonotone simulated annealing technique and Armijo line search, we propose a modified three-term conjugate gradient method to reduce the numbers of line search method used. For a given trial stepsize, we decide whether to accept it by simulated annealing rule; If not accepted, Armijo line search is then utilized. Under some mild conditions, the global convergence of the proposed method is established without the gradient Lipschitz continuous condition. Compared to some existing methods for unconstrained optimization problems, numerical experiments demonstrate that the proposed algorithm is promising for the testing problems.
五、報告題目：Adaptive stepsize for Douglas-Rachford splitting algorithm and ADMM
報告人簡介：
徐玲玲，南京師范大學數(shù)學科學學院副教授，碩士生導師。主要從事最優(yōu)化理論與算法方面的研究，主持國家自然科學基金青年基金一項，江蘇省高校自然科學基金一項，目前主持國家自然科學基金面上基金一項，科學與工程計算國家重點實驗室開放課題(重點)一項，參加國家重點研發(fā)計劃一項，擔任中國運籌學會宣傳委員會副主任、江蘇省運籌學會常務(wù)副秘書長等職。
報告內(nèi)容簡介：
The Douglas-Rachford (DR) splitting algorithm is a classical first-order splitting algorithm for solving maximal monotone inclusion problems. We propose an adaptive stepsize for DR splitting algorithm (ADR), which sets the step size based on local information of the objective function, and only requires two extra function evaluations per iteration. We prove the global convergence of ADR and the sublinear convergence rate of the objective function value in the ergodic sense. In addition, we apply ADR to solve the dual problem of the separable convex optimization problem with linear equality constraints and obtain an alternating direction method of multipliers with line search (ADMM-LS). By demonstrating the relationship between ADR and ADMM-LS, we prove the global convergence of ADMM-LS. Finally, we test three numerical experiments to compare the ADR and ADMM-LS with other algorithms. The numerical results verify the effectiveness and efficiency of ADR and ADMM-LS.
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燕山大學理學院
2024年9月20日
