Research

Research Interests

My research interests span theoretical, computational, and applied aspects of mathematical optimization.

My current focus is on convex programming and polynomial optimization in the abstract, and numerical methods for improving radiation therapy delivery to cancer patients. I also work on developing efficient algorithms for optimization problems under uncertainty arising in engineering, statistics, and health care.

My Google Scholar profile.

If you are a highly motivated graduate/undergraduate student interested in my work, send me an email! I have an open, funded, RA position for PhD students interested in research in large-scale deterministic and stochastic numerical optimization. You would likely enjoy this if you liked courses such MA 580, 505, 706, or 523.

Grants, Patent, and Software

My research is generously funded by the National Science Foundation. Active research grants:

  • Practical large-scale sum-of-squares optimization; NSF-DMS-1719828.
  • CAREER: Large-scale optimization problems with applications in emerging radiotherapy modalities; NSF-DMS-1847865.

My open-source Matlab package for general non-symmetric conic optimization using a primal-dual Newton-type method is available on GitHub. Joint work with Sercan Yildiz.

Some of my radiotherapy research is incorporated in a patent, joint with Philips Radiation Oncology Systems. (WO/2016/116868)

Publications

  1. Papp, D; Yildiz, S: Sum-of-squares optimization without semidefinite programming. 
    SIAM Journal on Optimization 29(1), 2019, pp. 822-851.
    [journal link]  |  [preprint PDF]  |  [supplementary material]  |  [Matlab code - alfonso]
  2. Gaddy, M; Unkelbach, J; Papp, D: Robust spatiotemporal fractionation schemes in the presence of patient setup uncertainty.
    Medical Physics 46(7), 2019, pp. 2988-3000.
    [journal link]
  3. Papp, D: Semi-Infinite Programming.   (Invited review.)
    Wiley StatsRef-Statistics Reference Online, 2019.
    [journal link]
  4. Papp, D; Yildiz, S: On "A Homogeneous Interior-Point Algorithm for Non-Symmetric Convex Conic Optimization". 
    Technical Report
    [preprint PDF]  |  [Matlab code - alfonso]
  5. Gaddy, MR; Yildiz, S; Unkelbach, J; Papp, D: Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit. 
    Physics in Medicine and Biology 63(1), 2018, p. 015036.
    [journal link]  |  [preprint PDF]
  6. Unkelbach, J; Papp, D; Gaddy, MR; Andratschke, N; Hong, T; Guckenberger, M: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy. 
    Radiotherapy and Oncology 125(2), 2017, pp. 357-364.
    [journal link]
  7. Papp, D: Semi-infinite programming using high-degree polynomial interpolants and semidefinite programming. 
    SIAM Journal on Optimization (27)3, 2017, pp. 1858-1879.
    [preprint PDF]  |  [journal link]
  8. Gaddy, MR; Papp, D: Improving the VMERGE treatment planning algorithm for rotational radiotherapy. 
    Medical Physics 43(7), 2016, pp. 4093-4097.
    [journal link]
  9. Papp, D: On the complexity of local search in unconstrained quadratic binary optimization. 
    SIAM Journal on Optimization 26(2), 2016, pp. 1257-1261.
    [preprint PDF]  |  [journal link]
  10. Chen, S; Mehrotra, S; Papp, D: Scenario generation for stochastic optimization problems via the sparse grid method. 
    Computational Optimization and Applications 62(3), 2015, pp. 669-692.
    [preprint PDF]  |  [journal link]
  11. Papp, D; Bortfeld, T; Unkelbach, J: A modular approach to intensity-modulated arc therapy optimization with noncoplanar trajectories. 
    Physics in Medicine and Biology 60(13), 2015, pp. 5179-5198.
    [journal link]
  12. Unkelbach, J; Papp, D: The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model. 
    Medical Physics 42(5), 2015, pp. 2234-2241.
    [journal link]
  13. Unkelbach, J; Alber, M; Bangert, M; Bokrantz, R; Bortfeld, T; Chen, D; Craft, D; Li, R; Men, C; Nill, S; Papp, D; Romeijn, E; Salari, E, Xing, L: Optimization approaches to volumetric modulated arc therapy planning.  (Invited review.)
    Medical Physics 42(3), 2015, pp. 1367-1377.
    [journal link] (open access)
  14. Mehrotra, S; Papp, D: A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization.  
    SIAM Journal on Optimization. 24(4), 2014, pp. 1670-1697.
    [preprint PDF]  |  [journal link]
  15. Craft, D; Bangert, M; Long, T; Papp, D; Unkelbach, J: Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset. 
    GigaScience 3, 2014, pp. 1-12.
    [journal link]  |  [Link to the CORT dataset]
  16. Unkelbach, J; Craft, D; Hong, T; Papp, D; Ramakrishnan, J; Salari, E; Wolfgang, J; Bortfeld; T: Exploiting tumor shrinkage through temporal optimization of radiotherapy. 
    Physics in Medicine and Biology 59(12), 2014, pp. 3059-3079.
    [preprint PDF]  |  [journal link]
  17. Craft, D; Papp, D; Unkelbach, J: Plan averaging for multicriteria navigation of sliding window IMRT and VMAT.
    Medical Physics 41(2), 2014, pp. 021709.
    [preprint PDF]  |  [journal link]
  18. Papp, D; Unkelbach, J: Direct leaf trajectory optimization for volumetric modulated arc therapy planning with sliding window delivery. 
    Medical Physics 41(1), 2014, pp. 011701.
    [preprint PDF]  |  [journal link]
  19. Papp, D; Alizadeh, F: Shape constrained estimation using nonnegative splines. 
    Journal of Computational and Graphical Statistics 23(1), 2014, pp. 211-231.
    [preprint PDF]  |  [journal link]
  20. Papp, D; Alizadeh, F: Semidefinite characterization of sum-of-squares cones in algebras. 
    SIAM Journal on Optimization 23(3), 2013, pp. 1398-1423.
    [journal link]
  21. Mehrotra, S; Papp, D: Generating moment matching scenarios using optimization techniques.
    SIAM Journal on Optimization 23(2), 2013, pp. 963-999.
    [preprint PDF]  |  [journal link]
  22. Alizadeh, F; Papp, D: Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming. 
    Annals of Operations Research 208(1), 2013, pp. 291-308.
    [journal link]
  23. Mehrotra, S; Papp, D: Generating nested quadrature formulas for general weight functions with known moments.
    Technical report, 2012.
    [PDF]
  24. Papp, D: Optimal designs for rational function regression. 
    Journal of the American Statistical Association 107(497), 2012, pp. 400-411.
    [preprint PDF]  |  [journal link]
  25. Tóth, J; Nagy, AL; Papp, D: ReactionKinetics - A Mathematica package with applications. 
    Chemical Engineering Science 83, December 2012, pp. 12-23.
    [journal link]
  26. Collado, R.A; Papp, D; Ruszczynski, A: Scenario decomposition of risk-averse multistage stochastic programming problems. 
    Annals of Operations Research 200(1), November 2012, pp. 147-170.
    [preprint PDF]   |  [journal link]
  27. Collado, R.A; Papp, D: Network interdiction--models, applications, unexplored directions.
    RUTCOR Research Report, 4-2012.
    [PDF]
  28. Papp, D; Alizadeh, F: Multivariate arrival rate estimation by sum-of-squares polynomial splines and decomposition.
    Technical report, 2011.
    [preprint PDF]
  29. Rudolf, G; Noyan, N; Papp, D; Alizadeh, F: Bilinear optimality constraints for the cone of positive polynomials. 
    Mathematical Programming 129(1), September 2011, pp. 5-31.
    [preprint PDF]  |  [journal link]
  30. Boros, E; Gurvich, V; Makino, K; Papp, D: Acyclic, or totally tight, two-person game forms; characterization and main properties. 
    Discrete Mathematics 310(6-7), April 2010, pp. 1135-1151.
    [preprint PDF]  |  [journal link]
  31. Papp, D; Vizvári, B.: Effective solution of linear Diophantine equation systems with an application in chemistry. 
    Journal of Mathematical Chemistry 39(1), January 2006, pp. 15-31.
    [preprint PS]  |  [journal link]

Papers in peer-reviewed conference proceedings

  1. Papp, D.: Univariate polynomial optimization with sum-of-squares interpolants.Proceedings of 2016 Modeling and Optimization: Theory and Applications, Selected Contributions, Bethlehem, PA, USA, pp. 143-162.
  2. Papp, D.; Alizadeh, F.: Multivariate Arrival Rate Estimation using Semidefinite Programming.
    Proceedings of the 2011 Winter Simulation Conference, Phoenix, AZ, pp. 2777-2787.
    [PDF]
  3. Papp, D.: Optimal designs for rational function regressionProceedings of the 2011 Joint Statistical Meetings, Miami Beach, FL.
    See the (more complete) journal version preprint above.
  4. Molnár, E.; Papp, D.: Visualization of Nil-geometry: Modelling Nil-geometry in Euclidean Space with Software PresentationProceedings of the Dresden Symposium Geometry: Constructive and Kinematic, Dresden, Germany, November 2003.
    [PDF]
  5. Arató, P.; Juhász, S.; Mann, Z.Á., Orbán, A.; Papp, D.: Hardware-software partitioning in embedded system designProceedings of the 2003 IEEE International Symposium on Intelligent Signal Processing, Budapest, Hungary, pp. 197-202.
    [PDF]

Textbook

  1. Tóth, J; Nagy, AL; Papp, D: Reaction Kinetics: Exercises, Programs and Theorems.  Springer-Verlag New York, 2018. XXIV+469 pages. [publisher link]

Theses

  1. Optimization models for shape-constrained function estimation problems involving nonnegative polynomials and their restrictions, PhD thesis, Rutgers University, May 2011.
  2. Analysis of Petri Net-Based Models and their Applications in Reaction Kinetics, Diploma thesis, Budapest University of Technology.