Abdellatif MOUDAFI

Academic position


Research interest

Selected publications

Academic position

Full Professor
Team I&M

Contact Information

Aix-Marseille Universite
Laboratoire d'Informatique et Systemes
UMR CNRS 7020, Faculte des Sciences
Domaine Universitaire Saint-Jerome Marseille.

Telephone: 0491056048. Fax: 0491056033.

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  - HDR, Universite Montpellier II - January 1997
    Accreditation to supervise research in Mathematics

- Doctorat d'etat (PhD in Mathematics)
    Universite Hassan II-Mohammadia - July 1995

- Doctorat (PhD in Applied Mathematics)
    Universite Montpellier II - May 1991

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Research interests


- Coupling Algorithms and Approximation.
- Proximal (Inertial) Algorithms of Selection.

Nonlinear Analysis

- Solvability and Sensitivity of Variational Problems.
- Feasibiliy, Fixed-point and Equilibrium Problems.

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Publications     MathSciNet

  Copositivity meets D.C. optimization. To appear in Journal of Dynamics and Games (2021). With P.-E. Mainge (French West Indies-Martinique)
  A semi-alternating algorithm for solving nonconvex split equality problems. To appear in Numerical Functional Analysis and Optimization (2021).
  Regularization projection method for solving bilevel variational inequality problem, Vol. 15 Optimization Letters (2021) 205-229. En collaboration avec Dang Van Hieu (Vietnam).
  Byrne's extended CQ-algorithms in the light of Moreau-Yosida regularization, Applied Set-Valued Analysis and Optimization 3 (2021) No 1, 1-6.
  From Progressive Decoupling of Linkages in Variational inequalities to Fixed-point problems, Applied Set-Valued Analysis and Optim. Vol. 2 (2020) No 2, 159-173. With N. Lehdili, UM6P (Maroc).
  Difference of Two Norms-Regularizations for Q-Lasso, Applied Computing and Informatics (2020), Vol. 17 No. 1, 79-89.
  A DC Regularization of Split Minimization Problems, Applied Analysis and Optimization (2018) Vol. 2, N 2, p. 285-297. En collaboration avec Hong-Kun Xu (Chine).
  l1-l2 regularization of split feasibility problems, Numerical Algorithms (2018), Vol. 78, N 3, p. 739-757 With Aviv Gibali (Israel).
  Extensions of the CQ Algorithm for the Split Feasibility and Split Equality Problems. Journal of Nonlinear and Convex Analysis Vol 18 N 8 (2017) 1485-1496. With Ch. Byrne (USA).
  An Inertial Krasnoselskii Type Algorithm for Lipschitz Pseudo-contractive Mappings, to appear in Bulletin of Iranian Mathematical Society (2017).
  A Barycentric Projected-subgradient Algorithm for Equilibrium Problems, Journal of Nonlinear and Variational Analysis Vol 1, Issue 1, 1 (2017) 43-59. With Dang Van Hieu (Vietnam).
  From Implicit Convex Feasibility to Convex Minimization, Transactions on Mathematical Programming and Appli. Volume 5 (2017), Number 1, 60 - 80. With Aviv Gibali (Israel).
  A proximal method for equilibrium problems under growth condition, Afrika Matematika Vol 28 Issue 5-6 (2017) 669-676. With M.A. Noor (Pakistan).
  About Proximal Algorithms for Q-Lasso, Thai Mathematical Journal Vol 15, No 1 (2017) p. 1-7.
  Viscosity methods for some applied nonlinear analysis problems. Fixed-point theory and Graph Theory. Foundations and Integrative Approaches, Elsevier(2016) chap. 4, 139-185 with P.-E. Mainge.
  Critical point concepts: a fixed-point approach, Communications on Applied Nonlinear Analysis. Vol 23 N 4 (2016) 41-47.
  A new Approach of the Parallel sum: properties and algorithmic aspects, Communications on Applied Nonlinear Analysis. (2015) Volume 22, Number 2, 46-57. With M. Ramazannejady (Iran).
  A note on Quasi Split Null-point Feasibility Problems, Journal of Nonlinear Analysis and Optimization: Theory & Applications (2014) Vol. 5, No. 2, 111-116.
  Computing the resolvent of composite operators, CUBO A Mathematical Journal Vol. 16, N 3 October (2014) p. 87-96.
  About a regularization of split monotone inclusions with composite operators, PanAmercican Journal Volume 24(2014), Number 3, 82-90. En collaboration avec Yekini Shehu (Nigeria).
  Alternating CQ-algorithms for Split Common Fixed-point Problems. Journal of Nonlinear and Convex Analysis 15 (2014), p. 809-818.
  Split algorithms for new Implicit Feasibility Null-point Problems, Applied Mathematics & Information Sciences (2014) 8, No. 5, 2113-2118.. With M. A. Noor (Pakistan).
  Solving Proximal Split Feasibility Problems without prior knowledge of operator norms. Optimization Letters Volume 8, Issue 7 (2014), Page 2099-2110 With B. S. Takhur (Inde).
  On Proximal Split Feasibility Problems; Incursion in the nonconvex case, International Journal of Mathematics Research Vol. 1 (2013) N 1.
  A connection between Chidume iteration and the contraction-proximal point algorithm. Afrika Matematika (2013) DOI 10.1007/s13370-013-0192-0.
  About relaxed cocoercivity and its role in the convergence of proximal algorithms, Journal of the Egyptian Mathematical Society Vol. 23 (2013) N 3, p. 281-284. With Zhenyu Huang (Chine).
  Simultaneous Iterative Methods for split equality problems and Applications, Transactions on Mathematical Programming and Applications Vol. 1 (2013), N 2, p. 1-11. With E. Al-Shemas (Koweit).
  A relaxed alternating CQ-algorithm for convex feasibility problems, Journal Nonlinear Analysis, Theory, Methods & Applications 79 (2013) 117-121.
  Viscosity-type Algorithms for the Split Common Fixed-point Problem, Advances in Nonlinear Variational Inequalities Vol. 16 (2013), N 1, 61-68.
  On critical points of the difference of two maximal monotone operators, Afrika Matematika, Springer (2013), 1-7.
  A regularized hybrid steepest descent method for variational inclusions, in Numerical Functional Analysis and Optimization 33 No. 1 (2012) 1-9.
  A Penalization-Gradient algorithm for variational inequalities, Special Issue on Fixed Point Theory, Variational Inequalities and its Approximation Algorithms, International J. Mathematics and Mathematical Sciences Vol 2011 (2011), Article ID 305856, with Iman Al-Shemas (Koweit).
  A note on the split common fixed-point problem for quasi-nonexpansive operators, Journal Nonlinear Analysis, Theory, Methods & Applications 74 (2011) 4083-4087.
  Split monotone variational inclusions, Journal of Optimization, Theory and Applications 150 (2011) 275-283.
  A duality algorithm for solving general varaiational inclusions, Special Issue of Variational Inequalities, Complementarity Problems and their Algorithms and Applications, J. of Advanced Modeling and Optimization Vol 13, N2, (2011) 213-220.
  A sufficient condition for the stability of Browder-type strong convergence to fixed points of nonexpansive mappings, PanAmercican Journal, (2011) Vol. 21, No. 4, 67-72.
  Some extragradient methods for nonconvex quasi-variational inequalities, Bulletin of Mathematical Analysis and Appl. Vol. 3 Issue 1 (2011), 178-187. With M. A. Noor, K. I. Noor, E. Al-Said.
  The split common fixed-point problem for demi-contractive mappings, Inverse Problems 26 (2010), 587-600.
  Penalty Methods for a System of Constrained Variational Inequalities, Optimization Letters (2010), 1-8. En collaboration avec M.A. Noor.
  A new general approach to resolvent operators and proximal algorithms, Communications on Applied Nonlinear Analysis. 17 (2010) N2, p 45-52.
  The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions, Applied Mathematics Letters 23 (2010) 620-624..
  Partial complement method for approximating solutions of a primal dual fixed-point problem, Optimization Letters (2010) N4, 449-456 .
  Proximal methods for a class of bilevel monotone equilibrium Problems, Journal of Global optimization 47 (2010) Issue 2, 287-292.
  A proximal iterative approach to a nonconvex optimization Problem, Nonlinear Analysis, Theory, Methods & Applications 72 (2010), 704-709
  From alternating minimization algorithms and systems of variational inequalities to equilibrium problems, Communications on Applied Nonlinear Analysis., Vol. 16, No. 3 (2009), 31-35.
  On the convergence of splitting proximal methods for equilibrium Problems in Hilbert spaces, Journal Math. Anal. Appl. 359 (2009) 508-513
  A variable Krasnoselski-Mann algorithm for a new class of fixed-point problems, Numerical Functional Analysis and Optim. 28 (2009), 1347-1354
  Projection Methods for a System of Nonconvex Variational Inequalities, Nonlinear Analysis, Theory, Methods & Applications 71 (2009), 517-520.
  Coupling Viscosity Methods with the Extragradient Algorithm for solving equilibrium Problems, (with P.-E. Mainge), Journal of Nonlinear and Convex Analysis, (2008) Vol. 9, No. 2, 283-294.
  Conditioning and convergence of processes for equilibrium Problems, PanAmercican Journal, (2008) Vol. 18, No. 3, 95-102.
  On the difference of two maximal monotone operators: Regularization and algorithmic approaches, Journal of Applied Mathematics and Computation 202 (2008), 446-452.
  Weak convergence theorems for nonexpansive mappings and equilibrium Problems, J. Nonlinear and Convex Anal., (2008) Vol. 9, No. 1, 37-43.
  Convergence of new inertial proximal methods for DC programming, (with P.-E. Mainge), SIAM Journal on Optimization., (2008) Vol. 19, No. 1 397-413.
  On finite and strong convergence of a proximal method for equilibrium Problems, Numerical Functional Analysis and Optimization, (2007) 28 (11-12), 1347-1354.
  Strong convergence of an iterative method for hierarchical fixed-point problems, (with P.-E. Mainge), Pacific Journal of Optimization, (2007) Vol. 3, N 3 , 529-538.
  Krasnoselskii-Mann Iteration For Hierarchical Fixed-point Problems, Inverse Problems , (2007) N 23, 1635-1640.
  A Proximal Method for Maximal Monotone Operators via Discretization of a first order Dynamical System, (with P.-E. Mainge), Journal of Convex Analysis, (2007) Vol. 14, N 4, 869-878.
  Modified gradient-projection methods for critical points of a constrained nonconvex minimization problem, (with P.-E. Mainge), Communications on Appli. Nonlinear Anal., (2007) 14, N 3, 51-61.
  Towards viscosity approximations of hierarchical fixed-point problems, (with P.-E. Mainge), J. of fixed point theory and applications 2006 (2006) Article ID 95453, 10 pages.
  On the Convergence of an Approximate Proximal Method for DC Functions (with P.-E. Mainge), Journal of computational Mathematics, (2006), Vol. 24, N 4. 475-480.
  A remark on recent results for finding zeroes of accretive operators, Journal Applied Mathematics & Stochastic Analysis , 2006 (2006) Article ID 56704, 6 pages.
  Proximal Methods for a Class of Relaxed Nonlinear Variational Inclusions, Advances in Nonlinear Variational Inequalities, (2006), Vol. 9, N 2, 59-64.
  Convergence of a Proximal-type Method for DC Functions, Journal of Applied Functional Analysis, (2006), Vol. 1, N3, 285-291.
  A hybrid inertial projection-proximal method for variational inequalities, Journal of Inequalities in Pure and Applied Mathematics, (2004), Vol. 5, Issue 2, 1-13.
  An algorithmic approach to prox-regular variational inequalities, Journal of Applied Mathematics and Computation, (2004), Vol. 155, Issue 3, 845-852.
  A remark on the convergence of the Tikhonov regularization without monotonicity, Journal of Mathematical Inequalities and Applications, (2004), Vol. 7, N 2, 283-288.
  A perturbed inertial proximal method for maximal monotone operators, Communications on Applied Nonlinear Analysis., (2004), Vol. 11, N 3, 101-108.
  On the convergence of iterative schemes for multivalued quasi-variational inclusions (with M. A. Noor), Journal Positivity , (2004), Vol. 2004. Issue 1, 75-84.
  Second-order Differential Proximal Methods for Equilibrium Problems, Journal of Inequalities in Pure and Applied Mathematics, (2003), Vol. 4, N 1. Paper No.18.
  Approximate inertial proximal methods using the enlargement of maximal monotone operators (with E. Elisabeth), International J. of Pure and Applied Mathematics, (2003), Vol. 5, N 3, 283-299
  Convergence of a splitting inertial proximal method for monotone operators (with M. Oliny), Journal of Computational and Applied Mathematics (2003), Vol. 155, 47-454.
  Multivalued quasi-variationnal inequalities in Banach spaces, Journal of Inequalities in Pure and Applied Math. (avec M. A. Noor et B. Xu), (2002), Vol. 3, N 3. Paper No.36.
  Mixed equilibrium problems: Sensitivity analysis and algorithmic aspect, Computers & Mathematics with applications (2002), Vol. 44, 1099-1108.
  Ergodic convergence to a zero of the extended sum of monotone operators, Inherently parallel algorithms in feasibility and optimization and their applications. Elsevier Science Publishers, Amsterdam, The Netherlands, 2001, (en collaboration avec M. Thera).
  New convergence results for iterative methods to set-valued mixed variational inequalities, Math. Inequalities and Applications (2000), Vol. 3, N2, 1-9. (with M. A. Noor).
  Viscosity methods for fixed points problems, Journal of Mathematical Analysis and Applications, (2000), Vol. 241, N1, 46-55.
  A recession notion for a class of monotone Bivariate functions Serdica Mathematical Journal 26 (2000), 1001-1014.
  On the regularization of the sum of two maximal monotone operators, Journal Nonlinear Analysis, Theory, Methods & Applications, (2000), Vol. 42, N6, 1-6.
  Tikhonov fixed-point regularization, Lecture Notes in Economics and Math. Systems, 481 (2000), 320-328 Springer.
  Sensitivity analysis for variational inclusions by Wiener-Hopf equation techniques, Journal Applied Mathematics & Stochastic Analysis (1999), Vol. 12, N3, 223-232 (with M. A. Noor).
  Proximal and dynamical approaches to equilibrium problems, Lecture Notes in Economics and Math. Systems, 477, (1999), 187-201, Springer, (avec M. Thera)
  Proximal point algorithm extended to equilibrium problems, Journal of Natural Geometry , January & April issue (1999), 1-10.
  Finding the zero for the sum of two maximal monotone operators, Journal Optimization Theory & Applications, vol. 94, N2, (1997), 425-448. (with M. Théra).
  Well-behaved asymptotical convex-concave functions, Numer. Funct. Anal. Optim. , 18, N 9\& 10, (1997), 1013-1021.
  Combining the proximal algorithm and Tikhonov method, Optimization 37 (1996), 239-252, (with N. Lehdili).
  Combining the auxiliary problem principle with approximation methods, Lecture Notes in Economics and Math. Systems, 452, Springer-Verlag (1996), 196-213, (avec M. Thera).
  On the stability of the parallel sum of maximal monotone operators, Journal of Mathematical Analysis and Applications 199 (1996), 478-488.
  On the convergence of the proximal algorithm for saddle-point problems, Optimization 33 (1995), 191-200.
  A perturbed algorithm for solving variational inequalities, J. Mathematical Analysis Applications 185 (1994), 706-712, (with A. Hassouni).
  Solvability of variational problems in general Banach spaces, Series on Advances in Math. for Appl. Sciences (1994), 51-67, (avec H. Attouch et Z. Chbani).
  Recession notion and partial inverse operator, Numer. Funct. Anal. Optim. , 16, 5 \& 6, (1995), 751-754.
  Coupling the proximal algorithm and Tikhonov method, J. Nonlinear Times and Digest 1, No 2, (1994), 169-178.
  About saddle values of a class of well-behaved convex-concave functions, Optimization 30 (1994), 1-14.
  Parallel sum of nonlinear monotone operators and variational convergence, Journal Nonlinear Analysis, Theory, Methods & Applications, 23, No 12, (1994), 1507-1514.
  Coupling proximal methods and variational convergence, Mathematical Methods of Operations Research, (1993), 269-280.
  Quantitative stability analysis for maximal monotone operators and semi-groups of contractions, Journal Nonlinear Analysis, Theory, Methods & Applications, vol. 21, (1993), 697-723. (with H. Attouch et H. Riahi)

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