Office: Neill 409
Phone: (509) 335-7760
Fax: (509) 335-1188
Email: [MyFirstName] [DOT] [LastName] [AT] wsu [DOT] edu
Fall 2018 Office Hours: 9:30-11:30am Wed., 10-11am Thur., or by appointment.
I work in the area of mathematical optimization. My current interests include theory and algorithms for convex and nonconvex problems, especially those with a mixture of continuous and discrete structures. My studies are often motivated by optimization applications in high-dimensional statistics, operations research and machine learning. In my free time I like fitness training, skiing and hiking. Here is a version of my CV.
- 08/2013 - current Assistant Professor, Department of Mathematics and Statistics, Washington State University;
- 09/2011 - 08/2013 Research Associate, Optimization Theme, Wisconsin Institutes for Discovery, U. Wisc-Madison ;
- 08/2006 - 12/2011 Ph.D. in Applied Mathematical and Computational Sciences, University of Iowa;
Compact Disjunctive Approximations to Nonconvex Quadratically Constrained Programs
(code on github)
Decades of progresses in mixed-integer linear/second-order-cone programs (MILP/MISOCP) leads to very efficient and reliable algorithms and solvers. Most well-known commercial solvers, among others, include Gurobi and CPLEX widely used in academia and industry. On the other hand our current ability of globally solving Mixed-integer (nonconvex) quadratically constrained programs (MIQCP) is much more limited, as they involve a new level of difficulty: MIQCP is still highly nonconvex even with all integers fixed. We propose a new approach to approximate MIQCP to arbitrary precision by moderately larger MISOCP. This new approximation scheme exploits implicit symmetry and is very economical. Our numerical results with prototypical implementation show they can close a significant amount of gap left by state-of-the-art solvers on some difficult problems. Since any polynomial can be represented by a quadratic system with additional variables, this approach can be in principle extended to globally solve mixed-integer polynomial optimization to arbitrary precision.
On the Linear Convergence of Difference-of-convex Algorithms for Nonsmooth DC Programming
Submitted to Math. Prog.
Current focus in optimization research is shifting towards optimizing structured nonconvex nonsmooth functions, partially movtivated by successful applications in areas such as high-dimensional statistics, machine learning, etc. In this paper we consider minimizing a function that is the difference of two nonsmooth convex functions and consider algorithms converging to a strong type of stationary points, namely d(irectional)-stationarity. We identify key assumptions necessary for proving linear convergence rate for these algorithms. To the best of our knowledge, we are the first to achieve this on problems with studied structures and algorithms converging to d-stationarity.
On Integer and MPCC Representability of affine sparsity
Submitted to Operations Research Letters.
This paper considers under what conditions the affine sparsity constraints (ASC) studied in our previous paper "Structural properties of ..." can be formulated by using integer programs (IP) and mathematical programming with complementarity constraints (MPCC). Therefore in some applications problems with ASC may be solved by IP or NLP solvers.
A fast heuristic for tasks assignment in Manycore Systems with Voltage-Frequency Islands
The 3rd International Conference on Green Communications, Computing and Technologies, GREEN
Structrual properties of affine sparsity constraints
First online: May 4, 2018. https://doi.org/10.1007/s10107-018-1283-3
In statistical model selection, two conflicting goals exist: a model that explains the available data well, and a model that is ``simple" and conforming to context-specific assumptions and expert knowledge. A popular approach in contemporary statistics and machine learning is to use a composite optimization model to simultaneously discovering important features and estimating related parameters. However current approaches for combining such context-specific assumptions are ad hoc beyond the popular notion of "sparisty", e.g., only a small number of features should be used. If logical implications among features exist: e.g., "if this feature is selected than that one cannot be selected", then current methods may break down. This paper provides a rigorous approach, e.g., affine sparsity constraints (ASC), for capturing such logical structures in the optimization models.
Optimal Engergy-Aware Scheduling in VFI-enabled Multicore Systems
In Proceedings of the 19th International Conference on High Persformance Computing and COmmunications (HPCC)
An energy-constrained Makespace Optimization Framework in Fine- to Coarse-grain Partitioned Multicore Systems.
In Proceedings of the sixth International Conference on Green and Sustainable Computing Conference (IGSC)
- Relaxing Nonconvex Quadratic Functions by Multiple Adaptive Diagonal Perturbations 2016 SIAM Journal on optimization. 26(3):1962-1985.
- Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection Oct 2015 Submitted to Math. Prog.
- Semidefinite Approaches for MIQCP: Convex Relaxations and Practical Methods July, 2015 Proceeding of Modeling and Optimization: Theory and Applications, 2014.
- On Valid Inequalities for quadratic programming with continuous variables and binary indicators The 16th Conference on Integer Programming and Combinatorial Optimization Lecture Notes in Computer Science 7801 169-180 2013
- Reduced rank regression via adaptive nuclear norm penalization Biometrika 2013 10.1093/biomet/ast036
- Symmetric tensor approximation hierarchies for the completely positive cone SIAM Journal on Optimization 23 3 1850-1866 2013
- Separation and Relaxation for cones of quadratic forms Mathematical Programming, Series A 137 1-2 343-370 Feb 2013
- Separating Doubly Nonnegative and Completely Positive Matrices Mathematical Programming, Series A 137 1-2 131-153 Feb 2013
- Representing quadratically constrained quadratic programs as generalized copositive programs Operations Research Letters 40 3 203-206 May 2012
- A note on "5X5 completely positive matrices" Linear Algebra and its Applications 433 5 1001-1004 2010
Some unpubished manuscripts
- MATH564: Nonlinear Optimization I (Fall 2013) (Fall 2015) (Fall 2017)
- MATH 565: Nonlinear Optimization II (Spr 2014) (Spr 2018)
- MATH 420: Linear Algebra (Fall 2014) (Fall 2017)
- MATH 364: Principles of Optimization (Fall 2014) (Fall 2015) (Spr 2017)
- MATH464: Linear Optimization (Spr 2017)
- MATH 220: Introductory Linear Algebra (Spr 2015) (Spr 2016)
- International Symposium of Mathematical Programming, Bordeaux, Fr. 07/2018. (Presentation Slides.)
- West Coast Optimization Meeting Spring 2018, Seattle, WA.
- INFORMS optimization society meeting. 03/2018, Denver, CO.
- Mathematics Colloquium, U. of Idaho. Dec. 2017.
- 1st Biennial Meeting of SIAM Pacific Northwest Section. Oct. 2017.