Maicon Marques Alves' home page

      M. Marques Alves, Associate Professor


      Office:  Departamento de Matemática
                   Universidade Federal de Santa Catarina
                   Florianópolis, SC, Brasil
                   88040900
      Phone: +55 48 37213678
      E-mail: maicon.alves@ufsc.br


    Research interests.        

        Convex Analysis, Convex Optimization, Monotone Operators, Proximal Algorithms.

    Publications.        

  1. On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng's modified forward-backward methods with inertial effects, submitted, June 2018 (with R. T. Marcavillaca).
  2. Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng's F-B four-operator splitting method for solving monotone inclusions, Numerical Algorithms, to appear (with M. Geremia).
  3. On the convergence rate of the scaled proximal decomposition on the graph of a maximal monotone operator (SPDG) algorithm, Optimization, to appear (with S. C. Lima). doi : 10.1080/02331934.2018.1476860.
  4. Pointwise and ergodic convergence rates of a variable metric proximal ADMM, Journal of Optimization Theory and Applications (2018), no. 2, 448-478 (with M.L.N. Goncalves and J. G. Melo). doi : 10.1007/s10957-018-1232-6.
  5. A proximal-Newton method for unconstrained convex optimization in Hilbert spaces, Optimization 67 (2018), no. 1, 67-82 (with B. F. Svaiter). doi : 10.1080/02331934.2017.1389942.
  6. An inexact Spingarn's partial inverse method with applications to operator splitting and composite optimization, Journal of Optimization Theory and Applications 175 (2017), no. 3, 818-847 (with S. C. Lima). doi : 10.1007/s10957-017-1188-y.
  7. Iteration-complexity of a Rockafellar's proximal method of multipliers for convex programming based on second-order approximations, submitted, December 2015; first revision, September 2016; second revision, April 2018 (with R.D.C.Monteiro and B.F.Svaiter).
  8. Regularized HPE-type methods for solving monotone inclusions with improved pointwise iteration-complexity bounds, SIAM Journal on Optimization 26 (2016), no. 4, 2730-2743 (with R.D.C.Monteiro and B.F.Svaiter). doi : 10.1137/15M1038566.
  9. A variant of the hybrid proximal extragradient method for solving strongly monotone inclusions and its complexity analysis, Journal of Optimization Theory and Applications 168 (2016), no. 1, 198-215 (with B.F.Svaiter). doi : 10.1007/s10957-015-0792-y.
  10. On the identification of piecewise constant coefficients in optical diffusion tomography by level set, ESAIM: Control, Optimisation and Calculus of Variations 23 (2017) 663-683 (with J.P. Agnelli, A. De Cezaro and A. Leitão). doi : 10.1051/cocv/2016007.
  11. A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity O(1/n^2), Journal of Convex Analysis 23 (2016), no. 1, 139-180 (with H. Attouch and B.F.Svaiter).
  12. Lower limits of type (D) monotone operators in general Banach spaces, Journal of Convex Analysis 23 (2016), no. 2, 333-345 (with O. Bueno and Y. Garcia ).
  13. Primal-dual regularized SQP and SQCQP type methods for convex programming and their complexity analysis, unpublished manuscript, April 2014 (with R.D.C.Monteiro and B.F.Svaiter).
  14. A note on Fejér-monotone sequences in product spaces and its applications to the dual convergence of augmented Lagrangian methods, Mathematical Programming (2016), no. 1, 613-616 (with B.F.Svaiter). doi : 10.1007/s10107-014-0849-y.
  15. Strong convergence in Hilbert spaces via \Gamma-duality, Journal of Optimization Theory and Applications 158 (2013), no. 2, 343-362 (with J.G. Melo). doi : 10.1007/s10957-012-0253-9.
  16. On Landweber-Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces, Inverse Problems 28 (2012), 104008 (with A. Leitão). doi : 10.1088/0266-5611/28/10/104008.
  17. A new qualification condition for the maximality of the sum of maximal monotone operators in general Banach spaces, Journal of Convex Analysis 19 (2012), no. 2, 575-589 (with B.F.Svaiter).
  18. Fixed points of generalized conjugations, Journal of Convex Analysis 18 (2011), no. 2, 577-588 (with B.F.Svaiter).
  19. On the surjectiviy properties of perturbations of maximal monotone operators in non-reflexive Banach spaces, Journal of Convex Analysis 18 (2011), no. 1, 209-226 (with B.F.Svaiter).
  20. Moreau-Yosida regularization of maximal monotone operators of type (D), Set-Valued and Variational Analysis 19 (2011), no. 1, 97-106 (with B.F.Svaiter).
  21. Multiple level-sets for elliptic Cauchy problems in three dimensional domains, Journal of Physics: Conference Series 255 (2010), 012005 (with A. Leitão).
  22. On Gossez type (D) maximal monotone operators, Journal of Convex Analysis 17 (2010), no. 3 & 4, 1077-1088 (with B.F. Svaiter).
  23. Maximal monotonicity, conjugation and the duality product in non-reflexive Banach spaces, Journal of Convex Analysis 17 (2010), no. 2, 553-563 (with B.F.Svaiter).
  24. A new old class of maximal monotone operators, Journal of Convex Analysis 16 (2009), no. 4, 881-890 (with B.F.Svaiter).
  25. Maximal monotone operators with a unique extension to the bidual, Journal of Convex Analysis 16 (2009), no. 2, 409-421 (with B.F.Svaiter).
  26. On convex representations of maximal monotone operators in non-reflexive Banach spaces, Ph.D. Dissertation, IMPA preprint server C 80/2009, February 2009.
  27. Brondsted-Rockafellar property and maximality of monotone operators representable by convex functions in non-reflexive Banach spaces, Journal of Convex Analysis 15 (2008), no. 4, 693-706 (with B.F.Svaiter).
  28. A new proof for maximal monotonicity of subdifferential operators, Journal of Convex Analysis 15 (2008), no. 2, 435-438 (with B.F.Svaiter).
  29. On level set type methods for elliptic Cauchy problems, Inverse Problems 23 (2007), no. 5, 2207-2222 (with A. Leitão).

    Links.


Last update: September, 2018
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