M. Marques Alves

Associate Professor of Mathematics
Department of Mathematics
Federal University of Santa Catarina (UFSC)
Florianópolis, SC, Brazil
88040-900


Email: maicon.alves@ufsc.br
Phone: +55 48 37213678
ORCID iD: orcid.org/0000-0001-5734-6959
Google Scholar: M. Marques Alves
CV: Currículo Lattes (in portuguese)


I am a mathematician, working mainly in the field of mathematical optimization and related subjects in convex and nonlinear functional analysis. I obtained my PhD at IMPA (Rio) in 2009 under the supervision of Benar F. Svaiter.

My current research topics include:

Please visit Seminário de Otimização & Problemas Inversos da UFSC for information (in portuguese) on our regular seminar on Optimization & Inverse Problems.


Teaching:


Students:


Recent talks and short courses:


Publications and working papers:

  1. Projective splitting with backward, half-forward and proximal-Newton steps, Working paper, 2022.

  2. A new relative-error inexact ADMM splitting algorithm for convex optimization, Working paper, 2022 (with M. Geremia).

  3. A relative-error inertial-relaxed inexact projective splitting algorithm, Working paper, 2020; last revised in September 2022 (with M. Geremia and R. T. Marcavillaca).

  4. Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methods, Optimization Methods and Software, to appear. doi : 10.1080/10556788.2021.2022148.

  5. Another proof and a generalization of a theorem of H. H. Bauschke on monotone operators, Optimization (2022) 71(1):91-96. doi : 10.1080/02331934.2020.1858833.

  6. Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms, Computational Optimization and Applications (2020) 75(2):389-422 (with J. Eckstein, M. Geremia and J.G. Melo). doi : 10.1007/s10589-019-00165-y.

  7. On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng's modified forward-backward methods with inertial effects, Set-Valued and Variational Analysis (2020), Vol. 28, 301-325 (with R. T. Marcavillaca). doi : 10.1007/s11228-019-00510-7.

  8. On the convergence rate of the scaled proximal decomposition on the graph of a maximal monotone operator (SPDG) algorithm, Optimization (2020), Vol 69, 2371-2381 (with S. C. Lima). doi : 10.1080/02331934.2018.1476860.

  9. 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 (2019), Vol. 82, 263-295 (with M. Geremia). doi : 10.1007/s11075-018-0604-1.

  10. Iteration-complexity of a Rockafellar's proximal method of multipliers for convex programming based on second-order approximations, Optimization (2019), Vol. 68, 1521-1550 (with R.D.C.Monteiro and B.F.Svaiter). doi : 10.1080/02331934.2019.1597357.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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).

  18. 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 ).

  19. 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.

  20. 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).

  21. 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.

  22. 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.

  23. 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).

  24. Fixed points of generalized conjugations, Journal of Convex Analysis 18 (2011), no. 2, 577-588 (with B.F.Svaiter).

  25. 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).

  26. 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).

  27. Multiple level-sets for elliptic Cauchy problems in three dimensional domains, Journal of Physics: Conference Series 255 (2010), 012005 (with A. Leitão).

  28. On Gossez type (D) maximal monotone operators, Journal of Convex Analysis 17 (2010), no. 3 & 4, 1077-1088 (with B.F. Svaiter).

  29. 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).

  30. A new old class of maximal monotone operators, Journal of Convex Analysis 16 (2009), no. 4, 881-890 (with B.F.Svaiter).

  31. Maximal monotone operators with a unique extension to the bidual, Journal of Convex Analysis 16 (2009), no. 2, 409-421 (with B.F.Svaiter).

  32. On convex representations of maximal monotone operators in non-reflexive Banach spaces, Ph.D. Dissertation, IMPA preprint server C 80/2009, February 2009.

  33. 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).

  34. A new proof for maximal monotonicity of subdifferential operators, Journal of Convex Analysis 15 (2008), no. 2, 435-438 (with B.F.Svaiter).

  35. On level set type methods for elliptic Cauchy problems, Inverse Problems 23 (2007), no. 5, 2207-2222 (with A. Leitão)


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Last update: September, 2022
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