M. Marques Alves
Associate Professor of Mathematics
Department of Mathematics
Federal University of Santa Catarina (UFSC)
Florianópolis, SC, Brazil
Phone: +55 48 37213678
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:
- Proximal algorithms for convex optimization and for inclusions with monotone operators;
in particular, inexact relative-error criteria for subproblems.
- Several forms of operator splitting algorithms: alternating
direction method of multipliers (ADMM), Douglas-Rachford
splitting, Spingarn's proximal-decomposition, Tseng's forward-backward method,
projective splitting etc.
- Accelerated first- and second-order algorithms for convex
optimization and monotone inclusions.
- Applications in inverse problems and statistical learning.
Please visit Seminário de Otimização & Problemas Inversos da UFSC
for information (in portuguese) on our regular seminar on Optimization & Inverse Problems.
- Juan E. Navarro - PhD (current)
- Andrea J. Rujano - MSc (2022)
- Luiz H. Suzana - MSc (2022)
- Marina Geremia - PhD (2020)
- Raul T. Marcavillaca - PhD (2020)
- Samara C. Lima - PhD (2018)
- Asteroide Santana - MSc (2013)
- Samara V. Pieta - MSc (2013)
Recent talks and short courses:
Publications and working papers:
with backward, half-forward and proximal-Newton steps, Working paper, 2022.
A new relative-error inexact ADMM
splitting algorithm for convex
optimization, Working paper, 2022 (with M. Geremia).
A relative-error inertial-relaxed inexact projective
splitting algorithm, Working paper, 2020; last revised in September 2022 (with M. Geremia and R. T. Marcavillaca).
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.
Another proof and a generalization of a theorem of H. H. Bauschke
on monotone operators,
Optimization (2022) 71(1):91-96.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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 ).
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.
Primal-dual regularized SQP and SQCQP type methods for convex programming and their complexity analysis,
April 2014 (with R.D.C.Monteiro and B.F.Svaiter).
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 :
On Landweber-Kaczmarz methods for regularizing systems of ill-posed equations in
Inverse Problems 28 (2012), 104008 (with A. Leitão).doi :
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).
Fixed points of generalized conjugations,
Journal of Convex Analysis 18 (2011), no. 2, 577-588 (with B.F.Svaiter).
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).
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).
Multiple level-sets for elliptic
Cauchy problems in three dimensional domains,
Journal of Physics: Conference Series 255 (2010), 012005
(with A. Leitão).
On Gossez type (D) maximal monotone operators,
Journal of Convex Analysis 17 (2010), no. 3 & 4, 1077-1088
(with B.F. Svaiter).
Maximal monotonicity, conjugation and the
duality product in non-reflexive Banach spaces,
Journal of Convex Analysis 17 (2010), no. 2, 553-563
A new old class of
maximal monotone operators,
Journal of Convex Analysis 16 (2009), no. 4, 881-890 (with B.F.Svaiter).
Maximal monotone operators
with a unique extension to the bidual,
Journal of Convex Analysis 16 (2009), no. 2, 409-421 (with B.F.Svaiter).
On convex representations
of maximal monotone operators in non-reflexive Banach spaces, Ph.D. Dissertation, IMPA preprint server C 80/2009, February 2009.
Brondsted-Rockafellar property and
maximality of monotone operators representable by convex functions in non-reflexive Banach spaces,
Convex Analysis 15 (2008), no. 4, 693-706
A new proof for maximal
monotonicity of subdifferential operators,
Journal of Convex Analysis 15 (2008), no. 2, 435-438
On level set type methods for elliptic
Inverse Problems 23 (2007), no. 5, 2207-2222 (with A. Leitão)
Last update: September, 2022