Tim Hoheisel, McGill University - Associate Professor in Continuous Optimization

Address

805 Sherbrooke St West, Room 1114
Montréal, Québec, Canada H3A 0B9

Tel: 514-398-3807
tim.hoheisel@mcgill.ca

Research interests

My research lies at the intersection of continuous optimization and nonsmooth analysis and therefore between applied and pure mathematics. Hence, the problems on which I work can be motivated by a concrete application but also of purely conceptual interest.

Google Scholar

Research Gate

Editorial work

2023-: Mathematics of Operations Research, Associate Editor.

2023-: Open Journal of Mathematical Optimization, Associate Editor.

2021-2023: Journal of Convex Analysis, Guest Editor for a special issue on the occasion of Roger Wets' 85th birthday.

2015-2021: Optimization, Associate Editor.

CRM Applied Math Lab and Seminar

As of July 2021, I am the director of the CRM Applied Math Laboratory.

Together with Simone Brugiapaglia (Concordia) and Jason Bramburger(Concordia) I am organizing the CRM Applied Math seminar hosted at McGill.

Memeberships

I am a scientific investigator at INTER-MATH-AI (IMA), a collaborative training program in Math and AI hosted by the University of Ottawa, McGill University, Université de Montréal and the University of Guelph, with partners the Research Institutes Fields and CRM (in Math) and Vector and MILA (in AI).

I am a core member of the MTL MLOpt group which is an assembly of researchers from the Montreal area working at the interface of optimization and machine learning.

I am a member of the CRM Applied Math Lab.

I am a member of SIAM (Society of Industrial and Applied Mathematics).

Some recent presentations

Foundations of Computational Mathematics (FoCM) 2023: Some applications of implicit function theorems from variational analysis .

IAM Distinguished Colloquium, University of British Columbia, Vancouver, September, 2022: The maximum entropy on the mean method for linear inverse problems .

One world Optimization Seminar , hosted at University of Vienna, September 2021: From perspective maps to epigraphical projections. A video of the talk can be found here .

Spring School on Variational Analysis, Paseky, May 2019: Topics in Convex Analysis (based on the lecture notes Topics in Convex Analysis in Matrix Space. )

Students and Postdocs

10/2022-: Matthew King-Roskamp, PhD student, (co-supervision with R. Choksi).

1/2021-: George Orfanides, PhD student (co-supervision with Adam Oberman).

Past

9/2021-: Quentin Fruytier, Masters student, (co-supervision with Abbas Khalili ).

9/2021-7/2023: Aaron Berk , Postdoc (co-supervision with Simone Brugiapaglia (Concordia) ).

9/2020-8/2022: Yakov Vaisbourd , Postdoc (co-supervision with Courtney Paquette)

10/2020-6/2021: Armand Gissler , Intern, ENS Paris-Saclay.

5/2019-9/2020: Gabriel Rioux, Masters student (co-supervision with R. Choksi). MSc. Thesis title: The Maximum Entropy on the Mean Method for Image Deblurring: Applying Fenchel-Rockafellar Duality in Finite and Infinite Dimensions. Currently a PhD student at Cornell.

9/2018-8/2020 : Quang Van Nguyen, Postdoc.

5/2018-8/2020 : Aram-Alexandre Pooladian, Masters student (co-supervision with A. Oberman). MSc. Thesis title: Numerical Methods for the Fermat-Weber Problem in the polyhedral l_p norms. Currently a PhD student at NYU.

9/2018-5/2020 : George Orfanides, Masters student, MSc. Thesis title: A Smoothing-Regularization Method for Mathematical Programs with Cardinality Constraints. After an internship at the Basque Center of Applied Mathematics (BCAM), Bilbao, he is now a PhD student.

Publications

Submitted for Publication

Y. Vaisbourd, R. Choksi, A. Goodwin, T. Hoheisel and C.-B. Schönlieb: Maximum Entropy on the Mean and the Cramer Rate Function in Statistical Estimation and Inverse Problems: Properties, Models, and Algorithms. Mathematical Programming, under revision.

Conference Proceedings

M. El Halabi, G. Orfanides, and T. Hoheisel: Difference of Submodular Minimization via DC Programming. International Conference on Machine Learning (ICML), 2023.

A. Pooladian, C. Finlay, T. Hoheisel, and A. Oberman: A principled approach to generating adversarial attacks under non-smooth dissimilarity metrics. Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.

Journal Articles

A. Berk, S. Brugiapaglia, and T. Hoheisel:Square Root LASSO: well-posedness, Lipschitz stability and the tuning trade off. SIAM Journal on Optimization, to appear.

A. Berk, S. Brugiapaglia, and T. Hoheisel:LASSO reloaded: a variational analysis perspective with applications to compressed sensing. SIAM Journal on Mathematics of Data Science 5(4), 2023, pp. 1102-1129.

T. Hoheisel and Elliot Paquette:Flatness of the nuclear norm sphere, simultaneous polarization, and uniqueness in nuclear norm minimization. Journal of Optimization Theory and Applications 197, 2023, pp. 252-276.

M.P. Friedlander, A. Goodwin, and T. Hoheisel: From perspective maps to epigraphical projections. Mathematics Operations of Research 48(2), 2023, pp. 1712-1740.

A. Gissler and T. Hoheisel: A note on the K-epigraph. Optimization 72, 2023, pp. 2251-2285.

T. Hoheisel, B. Pablos, A. Pooladian, L. Steverango, and A. Schwartz: A study of one-parameter regularizations for mathematical programs with vanishing constraints. Optimization Methods and Software 37(2), 2022, pp. 503-545.

M. Benko, M. Cervinka, and T. Hoheisel: Sufficient conditions for metric subregularity of constraint systems with applications to disjunctive and ortho-disjunctive programs. Set-valued and Variational Analysis 30, 2022, pp. 143-177.

J. V. Burke, T. Hoheisel, and Q. Van Nguyen: A study of convex convex-composite functions via infimal convolution with applications. Mathematics of Operations Research 46 (4), 2021, pp. 1235-1657.

G. Rioux, R. Choksi, T. Hoheisel, C. Scarvelis, and P. Maréchal: The Maximum Entropy on the Mean Method for Image Deblurring. Inverse Problems 37, 2021 (29 pp.).

G. Rioux, C. Scarvelis, R. Choksi, T. Hoheisel, and P. Maréchal: Blind Deblurring of Barcodes via Kullback-Leibler Divergence. IEEE Transactions on Pattern Analysis and Machine Intelligence 43(1), 2021, pp.77-88.

T. Hoheisel, M. Laborde, and A. Oberman: A regularization interpretation of the proximal point method for weakly convex functions. Journal of Dynamics and Games 7(1), 2020, pp. 79-96.

J. V. Burke, Y. Gao, and T. Hoheisel: Variational properties of matrix functions via the generalized matrix-fractional function. SIAM Journal on Optimization 29(3), 2019, pp. 1958-1987.

J. V. Burke, Y. Gao, and T. Hoheisel: Convex geometry of the generalized matrix-fractional function. SIAM Journal on Optimization 28(3), 2018, pp. 2189-2200.

J. V. Burke and T. Hoheisel: Epi-convergence properties of smoothing by infimal convolution. Set-valued and Variational Analysis 25(1), 2017, pp. 1-23.

J. V. Burke and T. Hoheisel: Matrix support functionals for inverse problems, regularization, and learning. SIAM Journal on Optimization 25(2), 2015, pp. 1135-1159.

Nadja Harms, Tim Hoheisel, and Christian Kanzow: On a smooth dual gap function for a class of player convex generalized Nash equilibrium problems. Journal of Optimization Theory and Applications 166(2), 2015, pp. 659–685.

N. Harms, T. Hoheisel, and C. Kanzow: On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities. Journal of Optimization Theory and Applications 163, 2014, pp. 413-438.

J. V. Burke and T. Hoheisel: Epi-convergent smoothing with applications to convex composite functions. SIAM Journal on Optimization 23(3), 2013, pp. 1457-1479.

J. V. Burke, T. Hoheisel, and C. Kanzow: Gradient consistency for integral-convolution smoothing functions. Set-valued and Variational Analysis 21(2), 2013, pp. 359-376.

W. Achtziger, T. Hoheisel and C. Kanzow: A smoothing-regularization approach to mathematical programs with vanishing constraints. Computational Optimization and Applications 55(3), 2013, pp. 733-767.

T. Hoheisel, C. Kanzow, and A. Schwartz: Theoretical and Numerical Comparison of Relaxation Methods for Mathematical Programs with Complementarity Constraints. Mathematical Programming 137, 2013, pp. 257-288.

W. Achtziger, C. Kanzow, and T. Hoheisel: On a relaxation method for mathematical programs with vanishing constraints. GAMM-Mitteilungen 35, 2012, pp. 110-130.

T. Hoheisel, C. Kanzow, and A. Schwartz: Mathematical Programs with Vanishing Constraints: A New Regularization Approach with Strong Convergence Properties. Optimization 61(6), 2012, pp. 619-636.

T. Hoheisel, C. Kanzow, B. S. Mordukhovich, and H. Phan: Generalized Newton's Method Based on Graphical Derivatives. Nonlinear Analysis Series A: Theory, Methods, and Applications 75(3), 2012, pp. 1324-1340.

T. Hoheisel, C. Kanzow, and A. Schwartz: Convergence of a local regularization approach for mathematical programs with complementarity or vanishing constraints. Optimization Methods and Software 27(3), 2012, 483-512.

T. Hoheisel, C. Kanzow, and A. Schwartz: Improved Convergence Properties of the Lin-Fukushima-Regularization Method for Mathematical Programs with Complementarity Constraints. Numerical Algebra, Control, and Optimization 1(1), 2011, pp.49-60.

T. Hoheisel, C. Kanzow and J. Outrata: Exact penalty results for mathematical programs with vanishing constraints. Nonlinear Analysis: Theory, Methods, and Applications 72, 2010, 2514-2526.

T. Hoheisel and C. Kanzow: On the Abadie and Guignard Constraint Qualification for Mathematical Programs with Vanishing Constraints, Optimization 58, Issue 4, 2009, pp. 431 - 448.

T. Hoheisel and C. Kanzow: Stationary Conditions for Mathematical Programs with Vanishing Constraints Using Weak Constraint Qualifications, Journal of Mathematical Analysis and Applications 337, 2008, pp. 292-310.

T. Hoheisel and C. Kanzow: First- and Second-Order Optimality Conditions for Mathematical Programs with Vanishing Constraints, Applications of Mathematics 52, 2007, pp. 495-514 (special issue dedicated to J.V. Outrata's 60th birthday).

Thesis

Mathematical Programs with Vanishing Constraints. Dissertation, Department of Mathematics, University of Wuerzburg, July 2009.

Other publications

James V. Burke and Tim Hoheisel: A note on epi-convergence of sums under the inf-addition rule. Optimization Online, 2015.

Book reviews

Featured Review of Convex Optimization: Introductory Course by Mikhail Moklyachuk. SIAM Review 66(1), p. 193-194.

Review of First-Order Methods in Optimization by Amir Beck. SIAM Review 61(2), p. 393.