Hongbo DongAssistant ProfessorOffice: Neill 409Phone: (509) 3357760Fax: (509) 3351188Email: [MyFirstName] [DOT] [LastName] [AT] wsu [DOT] edu Fall 2018 Office Hours: 9:3011:30am Wed., 1011am Thur., or by appointment. orcid.org/0000000319954608 
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 highdimensional statistics, operations research and machine learning. In my free time I like fitness training, skiing and hiking. Here is a version of my CV.
Positions/Education
 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. WiscMadison ;
 08/2006  12/2011 Ph.D. in Applied Mathematical and Computational Sciences, University of Iowa;
Current Teaching
 MATH416/516: Simulation Methods (Fall 2018 syllabus, Julia, Lecture Notes)
Selected Publications

Compact Disjunctive Approximations to Nonconvex Quadratically Constrained Programs
Submitted.
Nov 2018.
(code on github)
Decades of progresses in mixedinteger linear/secondordercone programs (MILP/MISOCP) leads to very efficient and reliable algorithms and solvers. Most wellknown commercial solvers, among others, include Gurobi and CPLEX widely used in academia and industry. On the other hand our current ability of globally solving Mixedinteger (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 stateoftheart 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 mixedinteger polynomial optimization to arbitrary precision.

On the Linear Convergence of Differenceofconvex 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 highdimensional 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 dstationarity.

On Integer and MPCC Representability of affine sparsity
Submitted to Operations Research Letters.
04/2018.
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 VoltageFrequency Islands
The 3rd International Conference on Green Communications, Computing and Technologies, GREEN
2018.

Structrual properties of affine sparsity constraints
Mathematical Programming
2018.
First online: May 4, 2018. https://doi.org/10.1007/s1010701812833
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 contextspecific 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 contextspecific 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 EngergyAware Scheduling in VFIenabled Multicore Systems
In Proceedings of the 19th International Conference on High Persformance Computing and COmmunications (HPCC)
2017.
DOI:10.1109/HPCCSmartCityDSS.2017.64

An energyconstrained Makespace Optimization Framework in Fine to Coarsegrain Partitioned Multicore Systems.
In Proceedings of the sixth International Conference on Green and Sustainable Computing Conference (IGSC)
2017.
DOI:10.1109/IGCC.2017.8323582
 Relaxing Nonconvex Quadratic Functions by Multiple Adaptive Diagonal Perturbations 2016 SIAM Journal on optimization. 26(3):19621985.
 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 169180 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 18501866 2013
 Separation and Relaxation for cones of quadratic forms Mathematical Programming, Series A 137 12 343370 Feb 2013
 Separating Doubly Nonnegative and Completely Positive Matrices Mathematical Programming, Series A 137 12 131153 Feb 2013
 Representing quadratically constrained quadratic programs as generalized copositive programs Operations Research Letters 40 3 203206 May 2012
 A note on "5X5 completely positive matrices" Linear Algebra and its Applications 433 5 10011004 2010
Some unpubished manuscripts

A mixedinteger framework for operational decisionmaking in sustainable nutrient management Feb 2017

On the exact recovery of sparse signals via conic relaxations Mar 2016
Previous Teaching
 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)
Recent News/Conferences
 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.