COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Hongbo Dong

Assistant Professor
Office: Neill 409
Phone: (509) 335-7760
Fax: (509) 335-1188

Email: [MyFirstName] [DOT] [LastName] [AT] wsu [DOT] edu

2019 Spr. Office Hours: 9:30-11:30am (Wed.), 9:30am-10:30am (Tue/Thur.), 3pm-5pm (Tue) 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 research projects are often motivated by problems in operations research/engineering, statistics and machine learning. In my free time I like fitness training, skiing and hiking. Here is a version of my CV.

Current Teaching
  • MATH220-01: Introductory Linear Algebra (Spr. 2019 syllabus)
  • MATH464: [CAPSTONE] Linear Optimization (Spr. 2019 syllabus)
Selected Publications
  1. Yaghoub Rahimi, Chao Wang, HD. and Yifei Luo A Scale Invariant Approach for Sparse Signal Recovery Submitted. Dec 2018.
  2. HD. and Yunqi Luo Compact Disjunctive Approximations to Nonconvex Quadratically Constrained Programs Submitted. Nov 2018. (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.

  3. Min Tao and HD. On the Linear Convergence of Difference-of-convex Algorithms for Nonsmooth DC Programming Submitted to Math. Prog. Aug 2018.

    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.

  4. HD. On Integer and MPCC Representability of affine sparsity Operations Research Letters. 47 (3) pp.208-212 May,2019.

    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.

  5. Hajiamini, S., Shirazi, B. and HD. A fast heuristic for tasks assignment in Manycore Systems with Voltage-Frequency Islands The 3rd International Conference on Green Communications, Computing and Technologies, GREEN 2018.
  6. HD. Miju Ahn and Jong-Shi Pang Structrual properties of affine sparsity constraints Mathematical Programming 2018. First online: May 4, 2018.

    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.

  7. S. Hajiamini, B. Shirazi, C. Cain and HD. Optimal Engergy-Aware Scheduling in VFI-enabled Multicore Systems In Proceedings of the 19th International Conference on High Persformance Computing and COmmunications (HPCC) 2017. DOI:10.1109/HPCC-SmartCity-DSS.2017.64
  8. S. Hajiamini, B. Shirazi, C. Cain and HD. 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) 2017. DOI:10.1109/IGCC.2017.8323582
  9. HD. Relaxing Nonconvex Quadratic Functions by Multiple Adaptive Diagonal Perturbations 2016 SIAM Journal on optimization. 26(3):1962-1985.
  10. HD., Kun Chen and Jeff Linderoth Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection Oct 2015 Submitted to Math. Prog.
  11. HD. and Nathan Krislock Semidefinite Approaches for MIQCP: Convex Relaxations and Practical Methods July, 2015 Proceeding of Modeling and Optimization: Theory and Applications, 2014.
  12. HD. and Jeff Linderoth 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
  13. Kun Chen, HD. and Kung-Sik Chan Reduced rank regression via adaptive nuclear norm penalization Biometrika 2013 10.1093/biomet/ast036
  14. HD. Symmetric tensor approximation hierarchies for the completely positive cone SIAM Journal on Optimization 23 3 1850-1866 2013
  15. Samuel Burer and HD. Separation and Relaxation for cones of quadratic forms Mathematical Programming, Series A 137 1-2 343-370 Feb 2013
  16. HD. and Kurt Anstreicher Separating Doubly Nonnegative and Completely Positive Matrices Mathematical Programming, Series A 137 1-2 131-153 Feb 2013
  17. Samuel Burer and HD. Representing quadratically constrained quadratic programs as generalized copositive programs Operations Research Letters 40 3 203-206 May 2012
  18. HD. and Kurt Anstreicher A note on "5X5 completely positive matrices" Linear Algebra and its Applications 433 5 1001-1004 2010
Some unpubished manuscripts
  1. Adam Christensen, HD., Jagdish Ramakrishnan, Mahmoud Sharara and Michael C. Ferris A mixed-integer framework for operational decision-making in sustainable nutrient management Feb 2017

  2. HD. On the exact recovery of sparse signals via conic relaxations Mar 2016

Previous Teaching

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