## Publications

*The electronic versions linked to below may differ from the published versions. Downloading is permitted for personal use only.*

- T. Haque, Y. Lucet. A Linear-Time Algorithm to Compute the Conjugate of Convex Piecewise Linear-Quadratic Functions . Submitted May 8, 2017.
- M. Jaberipour, W. Hare, Y. Lucet. Multi-fidelity surrogates for vertical alignment optimization in road design . Submitted December 13, 2017.

- D. Kumar, Y. Lucet. Computation of the Epsilon-Subdifferential of Convex Piecewise Linear-Quadratic Functions in Optimal Worst-Case Time. Submitted April 10, 2017. Accepted Feb 26, 2018 in Set-Valued and Variational Analysis. arxiv.org previous version.
- V. Beiranvand, W. Hare, Y. Lucet. Best Practices for Comparing Optimization Algorithms. Submitted June 3, 2016. Accepted Aug 23, 2017 in Optimization and Engineering; arviv.org previous version.
- A. Bajaj, W. Hare, Y. Lucet. Visualization of the $\epsilon$-subdifferential of Piecewise Linear-Quadratic Functions. Submitted June 6, 2016. Accepted January 11, 2017 in Computational Optimization and Applications; arxiv.org previous version.
- V. Beiranvand, W. Hare, Y. Lucet, S. Hossain. Multi-Haul Quasi Network Flow Model for Vertical Alignment Optimization. Submitted April 26, 2015. Accepted November 30, 2016 in Engineering Optimization; arxiv.org previous version.
- D. Hirpa, W. Hare, Y. Lucet, Y. Pushak, S. Tesfamariam. A bi-objective optimization framework for three-dimensional road alignment design. Submitted August 20, 2014. Accepted Jan 27, 2016 in Transportation Research Part C: Emerging Technologies; arxiv.org previous version.
- Y. Pushak, W. Hare, Y. Lucet. Multiple-Path Selection for new Highway Alignments using Discrete Algorithms. Submitted October 23, 2014. Accepted July 16, 2015 in European Journal of Operational Research; arxiv.org previous version.
- S. Mondal, Y. Lucet, W. Hare. Optimizing horizontal alignment of roads in a specified corridor. Submitted August 15, 2014. Accepted May 29, 2015 in Computers & Operations Research; arxiv.org previous version.
- H. H. Bauschke, Y. Lucet, H. M. Phan. On the convexity of piecewise-defined functions. Submitted August 17, 2014. Accepted April 9, 2015 in ESAIM (European Series in Applied and Industrial Mathematics): Control, Optimisation and Calculus of Variations ; arxiv.org previous version.
- W. Hare, Y. Lucet, F. Rahman. A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction. Submitted Feb 1, 2013. Accepted August 24, 2014 in European Journal of Operational Research
- A. Offenwanger, Y. Lucet. ConEE: An Exhaustive Testing Tool to Support Learning Concurrent Programming Synchronization Challenges. Submitted August 31, 2013. Conference on May 2-4, 2014. Published in Proceedings of the Western Canadian Conference on Computing Education, WCCCE '14.
- I. Rahmanian, Y. Lucet, S. Tesfamariam. Optimal Design of Reinforced Concrete Beams: A Review. Submitted May 10, 2013. Accepted in Computers and Concrete, An International Journal on Feb 2, 2014.
- W. Hare; S. Hossain, Y. Lucet, F. Rahman. Models and strategies for efficiently determining an optimal vertical alignment of roads. Submitted April 13, 2013. Accepted in Computers & Operations Research on November 6, 2013.
- B. Gardiner, J. Khan, Y. Lucet. Computing the Partial Conjugate of Convex Piecewise Linear-Quadratic Bivariate functions. Submitted June 22, 2011. Accepted on October 21, 2013 in Computational Optimization and Applications 58(1), 249-272, 2014.
- W. Hare and Y. Lucet. Derivative-Free Optimization via Proximal Point Methods. Submitted March 16, 2011. Accepted in Journal of Optimization Theory and Applications on June 1, 2013.
- Y. Lucet. Techniques and Open Questions in Computational Convex Analysis. Submitted January 30, 2012. Accepted Jan 9, 2013 in Springer Proceedings in Mathematics & Statistics, Vol. 50, Computational and Analytical Mathematics, a special issue in Honor of Jonathan Borwein's 60th Birthday.
- H. H. Bauschke and Y. Lucet. WHAT IS the Fenchel Conjugate? Accepted Oct 4, 2011 in Notices of the AMS.
- B. Gardiner, Y. Lucet. Computing the Conjugate of Convex Piecewise Linear-Quadratic Bivariate functions. Submitted March 1, 2011. Accepted on November 7, 2011 in Mathematical Programming; 139(1), 161-184, 2013.
- W. Hare, V. Koch, Y. Lucet. Models and algorithms to improve earthwork operations in road design using mixed integer linear programming. Volume 215, Issue 2, 1 December 2011, Pages 470480. Submitted Aug 19, 2010. Accepted June 8, 2011 in the European Journal of Operational Research
- Y. Lucet. What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications,. SIGEST section of SIAM Review. Volume 52, Issue 3, pp. 505-542 (2010). Revised version submitted on March 11, 2010. Published August 5, 2010.
- B. Gardiner and Y. Lucet. Convex Hull Algorithms for Piecewise Linear-Quadratic Functions in Computational Convex Analysis. Volume 18, Numbers 3-4 (2010), 467-482. Submitted Feb 2010. Accepted on Aug 10, 2010 in Set-Valued and Variational Analysis.
- B. Gardiner and Y. Lucet. Graph-Matrix Calculus for Computational Convex Analysis. 2011, Volume 49, 243-259. Submitted Jan 2010. Accepted Aug 18, 2010 in the book "Fixed-Point Algorithms for Inverse Problems in Science and Engineering", part of the Springer Verlag series Optimization and Its Applications
- V. Koch, and Y. Lucet. A note on: Spline technique for modeling roadway profile to minimize earthwork cost. Volume 6, Number 2, pages 393 - 400, May 2010. Submitted August 14, 2009. Resubmitted (minor revisions) Jan 2010. Accepted in Journal of Industrial and Management Optimization (JIMO) on Jan 2010.
- V. Koch, J. Johnstone and Y. Lucet. Convexity of the Proximal Average. Volume 148, Number 1 (2011), 107-124. Submitted June 29, 2009. Accepted in Journal of Optimization Theory and Applications on June 14, 2010.
- B. Gardiner and Y. Lucet. Numerical Computation of Fitzpatrick Functions. Volume 16, Number 4. Submitted May 15, 2008; Accepted in Journal of Convex Analysis on January 7, 2009.
- Y. Lucet. What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications,. Volume 20, Number 1, Pages 216-250. Accepted in SIAM Journal of Optimization on December 2, 2008.
- H. H. Bauschke, R. Goebel, Y. Lucet and S. Wang. The Proximal Average: Basic Theory. Volume 19, Number 2, 766-785, 2008. Submitted in April 2007. Accepted March 5, 2008. Published on line July 3, 2008 in SIAM Journal of Optimization.
- H. H. Bauschke, Y. Lucet and S. Wang. Primal-Dual Symmetric Intrinsic Methods for Finding Antiderivatives of Cyclically Monotone Operators. (Submitted 2006, accepted July 2007.) SIAM Journal of Control and Optimization (SICON), Volume 46 Issue 6, Pages 2031-2051, 2007.
- Y. Lucet, H. H. Bauschke, and M. Trienis. The Piecewise Linear-Quadratic Model for Computational Convex Analysis Submitted in July 2006. Accepted in Computational Optimization and Applications on June 21, 2007. Published in Computational Optimization and Applications, Volume 43, Number 1 on May 8, 2009
- H. H. Bauschke, Y. Lucet, and M. Trienis. How To Transform One Convex Function Continuously Into Another. SIAM Review, Volume 50, Number 1, 115-132, 2008. (Accepted June 19, 2007).
- Y. Lucet, 2006. Fast Moreau Envelope Computation I: Numerical Algorithms Accepted for publication on November 29, 2006. Numerical Algorithms, Volume 43, Number 3, 235-249, November 2006.
- Y. Lucet, 2006. New Sequential Exact Euclidean Distance Transform Algorithms based on Convex Analysis. Accepted for publication on July 3, 2006 in a special issue of Image and Vision Computing, Volume 27, Issues 1-2, 37-44, 2009.
- J.-B. Hiriart-Urruty and Y. Lucet, 2006. Parametric computation of the Legendre-Fenchel Conjugate with application to the computation of the Moreau envelope Accepted for publication on June 7, 2006 in Journal of Convex Analysis, Volume 14, Number 3, 657-666, August 2007.
- Y. Lucet, 2005. A linear Euclidean distance transform algorithm based on the Linear-time Legendre Transform. Proceedings of the Second Canadian Conference on Computer and Robot Vision (CRV 2005), IEEE Computer Society Press, 262-267, May 2005.
- Y. Lucet and J. Ye, 2002. Sensitivity Analysis for the value function for Optimization Problems with Variational Inequalities Constraints. SIAM J. Control and Optim., 40(3):699-723. with Errata: Y. Lucet and J. Ye, 2002. Erratum: Sensitivity analysis of the value function for optimization problems with variational inequality constraints. SIAM J. Control and Optim., 41(4):1315-1319.
- J. Borwein, Y. Lucet, and B. Mordukhovich, 2000. Compactly Epi-Lipschitzian Convex Sets and Functions in Normed Spaces. Journal of Convex Analysis, 7, No. 2, 375-393
- Y. Lucet, 1997. Faster than the fast Legendre transform, the linear-time Legendre transform. Numerical Algorithms, 16(2):171-185. Code in Netlib.
- Y. Lucet, 1996. A fast computational algorithm for the Legendre-Fenchel transform. Computational Optimization and Applications, 6(1):27-57.

## Patent

- Method and System for Determining the Vertical Alignment of an Infrastructure Corridor, United States Patent Application 20130290071

## Numerical Library

The Computational Convex Analysis library is available. The latest version has been accepted in Scilab ATOMS on February 21, 2012.## Others

- S. Sarafrazi, J. Loeppky, Y. Lucet. A Survey on the Sensitivity Analysis Methods for Understanding Complex Models. June 4, 2015.
- B. Gardiner and Y. Lucet. A Coverage Testing Method for Scientific Languages. March 15, 2010.
- Y. Lucet. Hybrid Symbolic-Numeric Algorithms for Computational Convex Analysis. 6
^{th}International Congress on Industrial and Applied Mathematics, Zurich Switzerland, July 2007. Submitted October 16, 2007. Online Jan 29, 2009 - Y. Lucet, 1998. The Legendre-Fenchel conjugate: Numerical computation, preprint CECM 98:114. Simon Fraser University.