In this talk, we present a fast and robust algorithmic framework SSNAL for solving large scale lasso problems. SSNAL is a semismooth Newton based augmented Lagrangian algorithmic framework. We show that for lasso problems, both the primal and dual iteration sequences generated by SSNAL possess a remarkably fast linear convergence rate, which can even be superlinear asymptotically. We also conduct variational analysis to analyse the second order sparsity structure of the underlying problems and proposed efficient numerical techniques to exploit the structure in our algorithm. Numerical comparison between our approach and state-of-the-art solvers on real data sets are presented to demonstrate the high efficiency and robustness of our proposed algorithm in solving difficult large scale lasso problems. For example, for a problem with over 4 million features and 16000 samples, SSNAL can solve it in 20 seconds, while the best alternative solver took 2400 seconds. This talk is based on joint work with Professor Sun Defeng and Dr. Li Xudong.
Prof Toh is from the department of mathematics and in addition to his role as IORA research director. His research mainly focuses on the design, analysis and implementation of robust and efficient algorithms for convex programming, particularly large scale linear and convex quadratic semidefinite programming and their generalizations.
He had developed the general purpose software, SDPT3, for solving medium scale SDP. SDPT3 is currently used as the computational engine in the convex optimization modeling language CVX and also worked on designing efficient preconditioned iterative methods for large scale linear systems arising from finite element discretization of soil-structure interaction problems.
Please refer to one of his publications on A Newton-CG augmented Lagrangian method for semidefinite programming -> Click here
(Held on the 29th Sept 2017)
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history of the point process. Hawkes process has wide applications in finance, social networks, neuroscience, criminology, seismology, and many other fields. In this paper, we prove a functional central limit theorem for stationary Hawkes processes in the asymptotic regime where the baseline intensity is large. The limit is a non-Markovian Gaussian process with dependent increments. We use the resulting approximation to study an infinite-server queue with high-volume Hawkes traffic. We show that the queue length process can be approximated by a Gaussian process, for which we compute explicitly the covariance function and the steady-state distribution. We also extend our results to multivariate stationary Hawkes processes and establish limit theorems for infinite-server queues with multivariate Hawkes traffic. This is a joint work with Lingjiong Zhu from Florida State University.
Dr Xuefeng Gao is an Assistant Professor at the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. He received his B.S. in Mathematics from Peking University, China in 2008, and his Ph.D. in Operations Research from Georgia Institute of Technology, USA in 2013.
His research interests include applied probability, high frequency trading and queueing theory. His work has been selected as Finalist in the 2011 INFORMS Junior Faculty Interest Group (JFIG) paper competition.
Please refer to one of his publications on Optimal Order Exposure in a Limit Order Market -> Click here
Dr He Shuangchi is an Assistant Professor at the Department of Systems Engineering and Engineering Management, National University of Singapore. He received his Ph.D. degree from Georgia Institute of Technology in 2011. His research interests include stochastic modeling and analysis, queueing theory, and statistical signal processing
His work has been selected as Third Place, INFORMS Junior Faculty Interest Group Paper Competition in 2015 and currently as Principal Investigator for the research on “Optimal control of surgery waiting lists".
Please refer to one of his publications on Many-server queues with customer abandonment: Numerical analysis of their diffusion model -> Click here
(Held on the 13th Oct 2017)
Industry 4.0: Challenges and Opportunity for Simulation Optimization
In this talk, we will discuss how industry 4.0 has brought in new challenges and opportunities for research in the area of simulation optimization. We will also present some latest work in simulation optimization and discuss the future research directions of this work in order to address the new challenges brought by the industry 4.0.
Prof Lee is an Associate Professor in the Department of Industrial and Systems Engineering at National University of Singapore and was a visiting professor at the Department of Systems Engineering and Operations Research at George Mason University. Dr Lee has also been appointed as the Eastern Scholar Professor for the Shanghai Maritime University by the Shanghai Municipal Education Commission. He received his B.S (Electrical Engineering) degree from the National Taiwan University in 1992 and his S.M and PhD degrees in 1994 and 1997 from Harvard University.
He has published more than 100 papers in international journals and has served as the associate editor for IEEE Transactions on Automatic Control, IIE Transactions, IEEE Transactions on Automation Science and Engineering, Flexible Services and Manufacturing Journal, Simulation: Transactions of The Society for Modeling and Simulation International, the Asia Pacific Journal of Operational Research, International Journal of Industrial Engineer: Theory, Applications and Practice. He is currently the co-editor for Journal of Simulation and is a member in the advisory board for OR Spectrum. He is a senior member of IEEE, and has served as a council member in the simulation society of INFORMS. His research focuses on the simulation-based optimization, maritime logistics which includes port operations and the modeling and analysis for the logistics and supply chain system. He has co-lead a team to win the grand prize for the next generation container port challenge in 2013 by proposing a revolutionary double storey container terminal design, called SINGA Port.
Please refer to one of his publications on Inventory Control Policy for a Periodic Review System with Expediting -> Click here
(Held on the 27th Oct 2017)
Held on the 10th Nov 2017)
Markov chain methods for analyzing algorithms
We are interested in using Markov chain methods to establish convergence in probability for various algorithms in dynamic programming and optimization. We start by investigating simple "empirical" variants of classical value and policy iteration for dynamic programming. In this case, we show that the progress of these algorithms is stochastically dominated by an easy to analyze Markov chain, from which we can extract a convergence rate for the original algorithms. We continue by showing that this same line of reasoning covers several empirical algorithms in optimization as well. We argue that the advantage of this approach lies in its simplicity and intuitive appeal.
William B. Haskell is assistant professor in the department of Industrial and Systems Engineering at NUS. He earned his PhD in Operations Research from the University of California in 2011. His work emphasises three themes: risk-aware optimisation, sequential decision making, and data-driven decision making.
Please refer to one of his publications on Primal-Dual Algorithms for Optimization with Stochastic Dominance -> Click here
Dr Vincent is an assistant professor in the Department of Electrical & Computer Engineering and Department of Mathematics at NUS. He earned his PhD in Electrical Engineering and Computer Science (EECS) in 2011. His research interests include information theory, machine learning and statistical signal processing
He is also an associate editor for coding and communication theory for the journal IEEE Transactions on Communications. Dr Tan has won several awards for his work, including the A*STAR Philip Yeo Prize for Outstanding Achievement in Research in 2011 and the NUS Young Investigator Award in 2014.
The informativeness of k-means for learning mixture models
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the correct target clustering of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an optimal clustering which minimizes the sum-of-squared distance between each point and its cluster center. In this paper, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. We verify the correctness of our theorems using numerical experiments and demonstrate using datasets with reduced dimensionality significant speed ups for the time required to perform clustering.
Please refer to one of his publications on Second-order asymptotics for the classical capacity of image-additive quantum channels -> Click here
Dr He is currently an Assistant Professor at the Department of Industrial & Systems Engineering, National University of Singapore. Dr He’s research interests are in the areas of Stochastic Modeling, Analysis, Control Statistical and Adaptive Signal Processing. His current research works include Probability Theory, Applied Mathematics and Telecommunications Engineering. Dr He obtained his PhD in Operations Research from Georgia Institute of Technology.
Please refer to one of his latest publications on Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs -> Click here
Complete Resource Pooling In Open Shop Networks
In an open shop network, each customer needs to go through all stations once, but the order of visiting each station is irrelevant. Can this flexibility in service order give us an edge in reducing customer waiting times? In this paper, we consider an open shop network consisting of two stations. We find routing and sequencing policies that are asymptotically optimal when the open shop network is operated in heavy traffic. We prove that under the obtained scheduling policies, customer waiting times in an open shop network are asymptotically close to the waiting times in a GI/GI/2 queue with the same traffic intensity.
Dr Hu received his Ph.D. in Industrial Engineering from the University of Illinois at Urbana-Champaign (UIUC). Prior to that, he obtained his B.Sc. in Applied Mathematics from Sun Yat-sen University. He worked as a Research Summer Intern at IBM T.J. Watson Research Center in 2014. He is the recipient of Dobrovolny Scholarship and William A. Chittenden Award from UIUC.
Dr Hu current research focuses on the dynamic pricing problems with reference price models. In particular, his is interested in deriving qualitative insights on the optimal pricing strategies as well as developing computationally efficient algorithms. He is also interested in cooperative game theory and its application in supply chain management.
Stable and Monotonic Allocation in Risk Pooling Problems
In many practical scenarios, agents cooperate to enjoy the benefits of risk pooling. Two notable examples are inventory pooling of news vendors and the risk sharing in, say, reinsurance market. A successful cooperation critically depends on how one allocates the costs among the cooperating agents. One consideration is the stability issue, i.e., no agent nor a coalition of agents should be better off by operating on its own. Another consideration is the monotonicity issue, i.e., as a new agent joins the coalition, every member in the coalition should be better off. In this talk, I will discuss these two issues in the cooperation of newsvendors as well as the risk sharing problem.
Please refer to one of his latest Publications on "Are Markets with Loss-Averse Consumers More Sensitive to Losses?" -> Click here
Hong Ming is currently a PhD student with the Institute of Operations Research and Analytics. He was formerly a lecturer with Temasek Polytechnic under the Mathematics and Statistics Division. He graduated from NUS with a Master of Science by Research degree and was a tutor for MA1505 Mathematics I and MA1101R Linear Algebra I. While pursuing his Bachelor of Science degree in NUS, Hong Ming took up Applied Mathematics as his primary major and Economics as his second major.
Hong Ming was awarded the Letter of Commendation for his outstanding performance as a Graduate Tutor during his Master’s study, and Bronze Award under the Senior Section from Singapore Mathematical Olympiads.
Investment Decisions and Falling Cost of Data Analytics
We study how the cost of data analytics and the characteristics of investors and investment opportunities affect investment decisions and their data analytics. We show that the falling cost of the data analytics raises investors’ leverage, financially constrained or highly risk averse investors use less data analytics, and the demand of data analytics is highest with high expected return opportunities. Due to the increased leverage, the falling cost of data analytics leads to higher losses during the crises.
Please refer to Hong Ming’s personal homepage for more information about him -> Click here