# RESEARCH PAPERS

### preprints

- Rectifiability of self-contracted curves

in the Euclidean space and applications*Journal of Geometric Analysis*(to appear)

(with G. David, E. Durand-Cartagena & A. Lemenant - Cut-generating functions and
*S*-free sets

preprint 23 p., (UAB 05/2013)

(with M. Conforti, G. Cornuejols, C. Lemarechal & J. Malick) - Orthogonal Invariance and Identifiability

preprint 21 p.

(with D. Drusvyatskiy & A. S. Lewis) - On the structure of locally symmetric manifolds

preprint 24 p.

(with J. Malick & H. Sendov) - Spectral (Isotropic) Manifolds and Their Dimension

preprint 24 p.

(with J. Malick & H. Sendov)

### 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 convexoptimization
*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) - Gradient Dynamical Systems, Tame Optimization and Applications

Lecture Notes, Spring School on Variational Analysis

Paseky nad Jizerou, Czech Republic, April 20-24, 2009 - 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

(withA. 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 obtainedvia 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)