RESEARCH PAPERS

preprints

• Generalized Hessians of C^1,1-functions and second-order viscosity subjets
  preprint 18 p, (UAB 27/2009)
  (with L. Barbet & P. Soravia)
  
  
• Locally symmetric submanifolds lift to spectral manifolds
  preprint 43 p, (UAB 23/2009)
  (with J. Malick & H. Sendov)
  
  
• Continuity of set-valued maps revisited in the light of tame geometry
  preprint 21 p, (CRM preprint 856/maig 2009)
  (with C.H. Jeffrey Pang)
  
  
• Generic identifiability and second-order sufficiency in tame convex optimization
  preprint 18 p, (UAB 03/2009)
  (with J. Bolte &A. Lewis)
  
  
• Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions, J. Math. Pures Appl. (to appear)
  (with O. Ley & S. Sabourau)
  
  

2010

• 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
  
  

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)