# 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)

### 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**

(with J. Bolte, A. Lewis and M. Shiota) - Filling the gap between lower-
*C*^{1}and lower-*C*^{2}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 Analysi*s**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)