RESEARCH PAPERS

preprints

• ABB Theorems: results and limitations in infinite dimensions
  hal-04646828 (preprint 12p, 2024) ; arXiv 2407.10509 (preprint 12p, 2024)
  (with Carlo Alberto De Bernardi and Enrico Miglierina)
  
  
• Solving Nonlinear Absolute Value Equations
  hal-04473917 (preprint 20p, 2024)
  (with M. Haddou, Tri Minh Le and O. Ley)
  
  
• Horofunction Extension and Metric Compactification
  hal-04786684 (preprint 30p, 2024)
  (with M. I. Garrido, J. Jaramillo and S. Tapia Garcia)
  
  

Accepted for publication

• All convex bodies are in the subdifferential of some
  everywhere differentiable locally Lipschitz function
  Proc. London Math. Society (in press)
  [DOI http://dx.doi.org/10.1112/plms.70007]
  (with Robert Deville and S. Tapia Garcia)
  
  
• A slope generalization of Attouch theorem
  Math. Programming (in press)
  [DOI https://doi.org/10.1007/s10107-024-02108-w]
  (with David Salas and S. Tapia Garcia)
  
  

2024

• Metric compatibility and determination in complete metric spaces
  Mathematische Zeitschrift 308:62, (2024)
  [DOI 10.1007/s00209-024-03609-2]
  (with Tri Minh Le and David Salas)
  
  
• Extending Rademacher Theorem to Set-Valued Maps
  SIAM J. Optim. 34 (2024), 1784-1798
  (with Marc Quincampoix)
  
  
• Oriented Calmness and Sweeping Process Dynamics
  Math. Oper. Res. 43 (2024), 1472-1486
  (with S. Tapia Garcia)
  
  
• Descent modulus and applications
  J. Funct. Anal. 287 (2024), Paper Number 110626
  (with Laurent Miclo and David Salas)
  
  
• Steepest geometric descent for regularized quasiconvex functions
  Set-Valued Var. Anal. 32 (2024), Paper number 28
  (with David Salas)
  
  

2023

• The slope robustly determines convex functions
  Proc. Amer. Math. Soc. 151 (2023), 4751-4756
  (with Dmitriy Drusvyatskiy)
  
  
• Extending the Choquet Theory: Trace convexity
  Houston Math. Journal 49 (2023), 247-282
  (with M. Bachir)
  
  

2022

• Determination of functions by metric slopes
  Proc. Amer. Math. Soc. 150 (2022), 4325-4333
  (with D. Salas)
  
  
• A convex function satisfying the Łojasiewicz inequality but failing
  the gradient conjecture both at zero and infinity
  Bull. London Math. Soc. 54 (2022), 590-608
  (with M. Haddou, O. Ley)
  
  
• Ubiquitous algorithms in convex optimization generate self-contracted sequences
  J. Convex Anal. 29 (2022) 119--128
  (with A. Böhm)
  
  

2021

• Characterizations of Filippov representable maps and Clarke subdifferentials
  Math. Programming 189 (2021), 99-115
  (with M. Bivas and M. Quincampoix)
  
  
• Asymmetric free spaces and canonical asymmetrizations
  Studia Mathematica 261 (2021), 55-102
  (with J.M. Sepulcre and F. Venegas M.)
  
  

2020

• Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds
  J. Funct. Anal. 279 (2020), 1-29
  (with J. Jaramillo and F. Venegas M.)
  
  
• Pathological subgradient dynamics,
  SIAM J. Optim. 30 (2020), 1327-1338
  (with D. Drusvyatskiy)
  
  

2019

• Linear structure of functions with maximal Clarke subdifferential
  SIAM J. Optim. 29 (2019), 511-521
  (with Gonzalo Flores)
  
  
• Metric and geometric relaxations of self-contracted curves
  J. Optim. Theory Appl. 182 (2019), 81-109
  (with R. Deville & E. Durand-Cartagena)
  
  
• Characterizations of Super-regularity and its Variants
  Chapter 6 (pp. 137--152) In:
  Splitting Algorithms, Modern Operator Theory and Applications, Springer, Cham 2019
  Print ISBN: 978-3-030-25938-9 (Springer, 2019)
  (with R. Luke and M. Tam)
  
  

2018

• Gradient flows, second order gradient systems and convexity
  SIAM J. Optim. 28 (2018), 2049-2066
  (with Tahar Boulmezaoud, Philippe Cieutat)
  
  
• Explicit formulas for C^1,1 Glaeser-Whitney extensions
  of $1$-Taylor fields in Hilbert spaces
  Proc. Amer. Math. Soc. 146 (2018), 4487-4495
  (with Mounir Haddou, Erwan Le Gruyer, Olivier Ley)
  
  
• A partial answer to the Demyanov-Ryabova conjecture
  Set-Valued Var. Anal. 26 (2018), 143-157.
  (with Colin Petitjean)
  
  
• Self-contracted curves in Riemannian manifolds
  J. Math. Anal. Appl. 457 (2018), 1333-1352
  (with R. Deville, E. Durand-Cartagena & L. Rifford)
  
  

2017

• Sweeping by a tame process
  Annales Institut Fourier 67 (2017), 2201-2223
  (with D. Drusvyatskiy)
  
  

2016

• Sard theorems for Lipschitz functions
  and applications in Optimization
  Israel Math. J. 212 (2016), 757-790
  (with L. Barbet & M. Dambrine & L. Rifford)
  
  
• Spectral (Isotropic) Manifolds and Their Dimension
  J. Anal. Math. 128, (2016) 369-397
  (with J. Malick & H. Sendov)
  
  

2015

• Cut-generating functions and S-free sets
  Math. Oper. Res. 40 (2015), 276-391
  (with M. Conforti, G. Cornuejols, C. Lemarechal & J. Malick)
  
  
• Stability in linear optimization under perturbations
  of the left-hand side coefficients,
  Set-Valued Var. Anal. 23 (2015), no. 4, 737-758.
  (with M.-A. Goberna, M. Lopez & R. Lucchetti)
  
  
• Rectifiability of self-contracted curves
  in the Euclidean space and applications
  J. Geom. Anal. 25 (2015), 1211-1239
  (with G. David, E. Durand-Cartagena & A. Lemenant)
  
  
• Orbits of geometric descent
  Canad. Math. Bull. 58 (2015), no. 1, 44-50
  (with D. Drusvyatskiy & A. S. Lewis)
  
  
• On the structure of locally symmetric manifolds
  J. Convex Anal. 22 (2015), 399-426
  (with J. Malick & H. Sendov)
  
  

2014

• Orthogonal Invariance and Identifiability
  SIAM J. Matrix Anal. Appl. 35 (2014), 580-598
  (with D. Drusvyatskiy & A. S. Lewis)
  
  

2013

• The Morse-Sard Theorem for Clarke critical values
  Advances in Mathematics 242 (2013), 217-227
  (with L. Barbet & M. Dambrine)
  
  
• Lower semicontinuity of the feasible set mapping
  of linear systems relative to their domains,
  Set-Valued Var. Anal. 21 (2013), 67-92
  (with M.-A. Goberna, M. Lopez & R. Lucchetti
  
  
• Cut Generation Functions
  IPCO XVI, M. Goemans and J. Correa (Eds)
  Lecture Notes in Computer Science 7801, Springer Heidelberg (2013), 123-132
  (with M. Conforti, G. Cornuejols, C. Lemarechal & J. Malick)
  
  

2012

• Modern Optimization Modelling Techniques
  Authors: J.-B. Lasserre, F. Facchinei, R. Cominetti
  Co-edited with J.-E. Martinez-Legaz
  Advanced Courses in Mathematics - CRM Barcelona
  Birkhäuser Verlag, Basel, 2011 (ISBN 978-3034802901)
  
  

2011

• Continuity and differentiability of set-valued maps
  revisited in the light of tame geometry
  J. London Math. Soc. 83 (2011), 637-658
  (with C.H. Jeffrey Pang)
  
  
• Generic identifiability and second-order sufficiency in tame convex optimization
  Math. Oper. Res. 36 (2011), 55-70 (with J. Bolte & A. Lewis)
  
  

2010

• Generalized Hessians of C^1,1-functions and second-order viscosity subjets
  SIAM J. Optim. 20 (2010), 340-352
  (with L. Barbet & P. Soravia)
  
  
• Asymptotic behaviour of self-contracted planar curves
  and gradient orbits of convex functions,
  J. Math. Pures Appl. 94 (2010), 183-199
  (with O. Ley & S. Sabourau)
  
  
• Characterizations of Lojasiewicz inequalities:
  subgradient flows, talweg, convexity
  Trans. Amer. Math. Soc. 362 (2010), 3319-3363
  (with J. Bolte, O. Ley & L. Mazet)
  
  

2009

• Identifying structure of nonsmooth convex functions by the bundle technique
  SIAM J. Optimization 20 (2009), 820-840
  (with M. Solodov & C. Sagastizábal)
  
  
• Tame functions are semismooth
  Math. Programming (Series B) 117 (2009), 5-19
  (with J. Bolte & A. Lewis)
  
  
• Subdifferential characterization of approximate convexity: the lower semicontinuous case
  Math. Programming (Series B) 116 (2009), 115-127
  (with F. Jules & M. Lassonde)
  
  
• Locally symmetric submanifolds lift to spectral manifolds
  preprint 43 p, (UAB 23/2009)
  (with J. Malick & H. Sendov)
  
  

2008

• On the first integral conjecture of René Thom
  Bull. Sci. Math 132 (2008), 625-631
  (with J. Cresson & M. Shiota)
  
  
• Prox-regularity of spectral functions and spectral sets
  Journal of Convex Analysis 15 (2008), 547-560
  (with A. Lewis, J. Malick, H. Sendov)
  [ Article dédié à la mémoire de Thomas Lachand-Robert ]
  
  

2007

• Clarke subgradients of stratifiable functions
  SIAM J. Optimization 18 (2007), 556-572
  (with J. Bolte, A. Lewis and M. Shiota)
  
  
• Stability of periodic solutions for Lipschitz systems obtained via the averaging method
  Proc. Amer. Math. Soc 135 (2007), 3317-3327
  (with A. Buica)
  
  
• The Lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
  SIAM J. Optimization 17 (2007), 1205-1223
  (with J. Bolte & A. Lewis)
  
  
• Remarks on the class of (semi)strictly quasiconvex functions
   J. Optim. Theory Appl. 133 (2007), 37-48
  (with Y. Garcia)
  
  

2006

• The Morse-Sard theorem for non-differentiable subanalytic functions
  J. Math. Anal. Appl. 321 (2006), 729-740
  (with J. Bolte & A. Lewis)
  
  
• On the Equivalence Between Complementarity Systems, Projected Dynamical Systems and Unilateral Differential Inclusions
  Systems & Control Letters 55 (2006), 45-51
  (with V. Acary, B. Brogliato & C. Lemarechal)
  
  
• Geometrical interpretation of the proximal-type algorithms in structured optimization problems
  Optimization 55 (2006), 481-503 (special issue for the 65th birthday of D. Pallaschke)
  (with W. Hare & J. Malick)
  
  

2005

• Subsmooth sets: functional characterizations and related concepts
  Trans. Amer. Math. Soc. 357 (2005), 1275-1301
  (with D. Aussel & L. Thibault) [Corrigendum (concerning the published version) ]
  
  
• Subdifferential representation of convex functions: refinements and applications
  J. Convex Analysis 12 (2005), 255-265
  (with J. Benoist)
  
  
• On a primal-proximal heuristic in discrete optimization
  Math. Programming 104 (2005), 105-128
  (with C. Lemarechal)
  
  
• Clarke critical values of subanalytic Lipschitz continuous functions
  Annales Polonici Mathematici 87 (2005), 13-25 (memorial issue for S. Lojasiewicz)
  (with J. Bolte, A. Lewis and M. Shiota)
  
  
• Filling the gap between lower-C¹ and lower-C² functions
  J. Convex Analysis 12 (2005), 315-329
  (with J. Malick)
  
  
• Comment on the article ''Generalized derivatives and nonsmooth optimization, a finite dimensional tour (Invited Survey)'' (by J. Dutta)
  TOP (Revista de Investigación Operativa publicada por la SEIO, Discussion Session, Volume 13, Number 2 (2005), 279-283
  
  

2004

• Approximate convexity and submonotonicity
  J. Math. Anal. Appl. 291 (2004), 292-301
  (with P. Georgiev)
  
  
• Cyclic hypomonotonicity, cyclic submonotonicity and integration
  J. Optim. Theory Appl. 122 (2004), 19-40
  (with P. Georgiev)
  
  

2003

• Integration of multivalued operators and cyclic submonotonicity
  Trans. Amer. Math. Soc. 355 (2003), 177-195
  (with P. Georgiev & J.-P. Penot)
  
  

2002

• Characterizations of evenly convex sets and evenly convex functions
  J. Math. Anal. Appl. 273 (2002), 58-66
  (with J.-E. Martinez-Legaz)
  
  
• Lower subdifferentiability and Integration
  Set-Valued Analysis 10 (2002), 89-108
  (with M. Bachir, J.-P. Penot)
  
  
• Integration of Fenchel Moreau subdifferentials of epi-pointed functions
  SIAM J. Optimization 12 (2002), 575-582
  (with J. Benoist)
  
  
• Coincidence theorems for convex functions
  J. Convex Analysis 9 (2002), 259-268
  (with J. Benoist)
  
  

2001

• Dual characterizations of relative continuity of convex functions
  J. Austral. Math. Soc. (Series A) 70 (2001), 211-223
  (with J. Benoist)
  
  
• Appropriate subdifferentials in quasiconvex analysis
  SIAM J. Optimization 12 (2001), 407-420
  (with N. Hadjisavvas & J.-E. Martinez-Legaz)
  
  
• Normal cones to sublevel sets: an axiomatic approach
  Lecture Notes in Econom. & Math. Systems 502 (2001), 88-101, (Springer, Berlin)
  (with D. Aussel)
  
  

2000

• A dual characterization of the Radon-Nikodym property
  Bull. Austral. Math. Soc. 62 (2000) 379-387
  (with M. Bachir)
  
  
• Arrow-Barankin-Blackwell theorems and related results in cone duality: a survey
  Lecture Notes in Econom. & Math. Systems 481 (2000), 119-131, (Springer, Berlin)
  
  
• On generalized cyclically monotone operators and proper quasimonotonicity
  Optimization 47 (2000), 123-135
  (with N. Hadjisavvas)
  
  
• Normal characterization of the main classes of quasiconvex functions
  Set-Valued Anal. 8 (2000), 219-236
  (with D. Aussel)
  
  
• Subdifferentials of convex functions and sigma-cyclic monotonicity
  Bull. Austral. Math. Soc. 61 (2000), 269-276
  
  

1996 - 1999

• Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions
  J. Optim. Theory Appl. 102 (1999), 525-536
  (with N. Hadjisavvas)
  
  
• On the subdifferentials of quasiconvex and pseudoconvex functions and cyclic monotonicity
  J. Math. Anal. Appl. 237 (1999), 30-42
  (with N. Hadjisavvas)
  
  
• Coercivity Conditions and Variational Inequalities
  Math. Programming 86 (1999), 433-438
  (with N. Hadjisavvas)
  
  
• Connectedness of the efficient set for three objective quasiconcave maximization problems
  J. Optim. Theory Appl. 93 (1997), 517-524
  (with N. Hadjisavvas & S.Schaible)
  
  
• Existence Theorems for Vector Variational Inequalities
  Bull. Austral. Math. Soc. 54 (1996), 473-481
  (with N. Hadjisavvas)