# YVES LUCET

## Publications

• M. Jaberipour, W. Hare, Y. Lucet. Multi-fidelity surrogates for vertical alignment optimization in road design . Submitted December 13, 2017.
1. T. Haque, Y. Lucet. A Linear-Time Algorithm to Compute the Conjugate of Convex Piecewise Linear-Quadratic Functions . Submitted May 8, 2017. Accepted April 9, 2018 in Computational Optimization and Applications
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. H. H. Bauschke and Y. Lucet. WHAT IS the Fenchel Conjugate? Accepted Oct 4, 2011 in Notices of the AMS.
18. 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.
19. 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 470480. Submitted Aug 19, 2010. Accepted June 8, 2011 in the European Journal of Operational Research
20. 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.
21. 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.
22. 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
23. 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.
24. 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.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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
30. 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).
31. 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.
32. 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.
33. 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.
34. 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.
35. 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.
36. 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
37. Y. Lucet, 1997. Faster than the fast Legendre transform, the linear-time Legendre transform. Numerical Algorithms, 16(2):171-185. Code in Netlib.
38. Y. Lucet, 1996. A fast computational algorithm for the Legendre-Fenchel transform. Computational Optimization and Applications, 6(1):27-57.

## Patent

1. 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

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