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Last Updated by January 2019

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Name Used in  Bibliographic Citations: J.Y. Bello Cruz   &   J.Y.B. Cruz  &   J.Y. Bello-Cruz

About Me: I am an Assistant Professor: Numerical Analysis and Optimization in the Department of Mathematical Sciences at Northern Illinois University (NIU)USA. Prior NIU I was an Assistant Professor (with tenure) in the Institute of Mathematics and Statistics at the Federal University of Goias, BrazilI worked from 2013 to 2015 with Prof. Heinz H. Bauschke as a CNPq Postdoctoral Research Fellow in the Irving K. Barber School of Arts and Sciences, Mathematics at the University of British Columbia, CanadaMy Ph.D. in Mathematics was supervised by Prof. Alfredo N. Iusem at the Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil. All my basic education, the 5 years Bachelor in Mathematics and the 2 years M.Sc. in Analysiswere coursed in the Faculty of Mathematics and Computer Science, University of Havana, Cuba.

My main research interest is in the area of Continuous Optimization, focusing on Nonsmooth and Convex Optimization, Variational Inequalities, Inclusion Problems, Algorithms, and Applications. My research is supported by the National Science Foundation (NSF) on the research Grant # DMS - 1816449 (September 2018 - August 2021) and by internal grants from NIU. For further details please see my CV.

Professional Address:  Department of Mathematical Sciences, Northern Illinois University. Watson Hall 366, DeKalb, IL, USA - 60115. 

Phones: +1 8157536764 (Office Number) or  8159818002 (Online Number)

Email: yunierbello at niu dot edu  or  yunier.bello at gmail dot com 



  • M.Sc. in Mathematics, University of Havana, Havana, Cuba (2005)                                         


  • ($ 99,143.00) NSF Grant - DMS - 1816449Second-Order Variational Analysis in Structured Optimization and Algorithms with Applications (2018 - 2021). USA.
  • ($ 8,000.00) Start-up Research Grant from Northern Illinois University. (2016 - 2017). USA.
  • Supported by CAPES - International Symposium on Mathematical Programming, Pittsburgh- PA. (July 2016). USA.
  • (R$ 36,000.00) Productivity Research Grant by CNPq - 303492/2013-9. Federal University of Goias. (2014 - 2016). Brazil.
  • Supported by CNPq - Research Visit to T.T.A. Nghia, Oakland University, Rochester Hills,  MI (3 weeks on July 2015). USA.
  • Postdoctoral Scholarship sponsorship by CNPq at the University of British Columbia. Grant 202677/2013-3(August 2013 - January 2015). Canada.
  • MATHAMSUD. Variational Analysis and its applications to optimization, monotone operators, convex analysis, and Nash equilibrium problems. Sponsorship by CAPES/ Centre National de la Recherche Scientifique (CNRS). Federal University of Goiás. 2013 - 2014.
  • (R$ 125,000.00) Project CAPES/MES-CUBA. "Modelos de Otimização e Aplicações". Sponsorship by CAPES. Federal University of Goiás. (2012 - 2016). Brazil.
  • Research Project PRONEX-CNPq/FAPERJ (26/2006 and 15/2009 - APQ1). "Núcleo de Excelencia em Teoria e Métodos de Otimização Contínua", Sponsorship by CNPq. (2007 - 2013). Brazil. 
  • Grant funds from CAPES for a visiting professor at University of Havana. (November 2012 - December 2012). Cuba.
  • Summer Postdoctoral Scholarship at Instituto de Matemática Pura e Aplicada. (Summer 2 months, 2011). Brazil.
  • Research Project PROCAD-nf (21/2009) from CAPESAnálise, Geometria e Otimização UFG/UNB/IMPA, Federal University of Goiás. (2010 - 2013). Brazil.
  • Summer Postdoctoral Scholarship at Instituto de Matemática Pura e Aplicada. (January 4 - February 26, 2010). Brazil.
  • P.C.I. Postdoctoral Scholarship at IMPA. (October 1 - 24, 2009). Brazil.
  • Financial Help from CONICYT for School on Variational Analysis at CMM, University of Chile. (November 6 - 19, 2008). Chile.
  • Ph.D. Scholarship under the sponsorship of CNPq-TWAS at IMPA. (August 2006 - July 2009). Brazil.
  • Financial Help of Mathematical Union for Latin America and the Caribbean (UMALCA) for participation in EMALCA, San Jose de Costa Rica. (February, 13 to 19, 2005). Costa Rica.
  • Financial Help of Centre International de Mathematiques Pures et Appliquees (CIMPA) for participation in EMALCA, Guanajuato. (August, 1 to 12, 2005). Mexico.

J.Y. Bello Cruz, G. LiT.T.A. Nghia
On the Q-linear convergence of forward-backward splitting method and uniqueness of optimal solution to Lasso. pp. 35, (2018). 

J.Y. Bello Cruz, G. Bouza Allende. 
An Inexact strategy for the projected gradient algorithm in vector optimization problems on variable ordered spaces. pp. 23, (2018). 

J.Y. Bello CruzR. Díaz MillánH.M. Phan
Conditional extragradient algorithms for solving constrained variational inequalities. pp. 28, (2017). 

R. Behling, J.Y. Bello CruzL. R. Santos.
On the linear convergence of the circumcentered-reflexion method. 
Operations Research Letters. 46, 159--162 (2018).  
 PDF  |  doi>
R. BehlingJ.Y. Bello CruzL. R. Santos.
Circumcentering the Douglas-Rachford method. 
Numerical Algorithms. 78, 759--776 (2018).  
 PDF  |  doi>

J.Y. Bello CruzY. Shehu.
An Iterative method for split inclusion problems without prior knowledge of operator norms. 
Journal of Fixed Point Theory and Applications. 19, 2017--2036 (2017).  
 PDF  |  doi>

J.Y. Bello Cruz
On proximal subgradient splitting method for minimizing the sum of two nonsmooth convex functions.
Set-Valued and Variational analysis. 25, 245--263 (2017). 
 PDF  |  doi>

J.Y. Bello CruzO.P. Ferreira, S.Z. Németh, L.F. Prudente.  
A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone.
Linear Algebra and its Applications. 513, 160--181 (2017). 
(MATLAB_codes).  PDF  |  doi>

J.Y. Bello CruzT.T.A. Nghia
On the convergence of the forward-backward splitting method with linesearches. 
Optimization Methods and Software. 31, 1209--1238 (2016). 
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Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces. 
Numerical Algorithms. 73, 33--76 (2016). 
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J.Y. Bello CruzO.P. FerreiraL.F. Prudente
On the global convergence of the inexact semi-smooth Newton method for absolute value equation.  
Computational Optimization and Applications. 65, 93--108 (2016). 
(MATLAB_codes).  PDF  |  doi>

J.Y. Bello CruzR. Díaz Millán
A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces.
Journal of Global Optimization. 65, 597--614 (2016)
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J.G. Barrios, 
J.Y. Bello CruzO.P. Ferreira, S.Z. Németh. 
A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex programming. 
Journal of Computational and Applied Mathematics. 301, 91--100 (2016). 
(MATLAB_codes).  PDF  |  doi>

J.Y. Bello CruzW. de Oliveira. 
On weak and strong convergence of the projected gradient method for convex optimization in real Hilbert spaces.  
Numerical Functional Analysis and Optimization. 37, 129--144 (2016).  
 PDF  |  doi>

W.V. Ackooij,  J.Y. Bello CruzW. de Oliveira. 
A strongly convergent proximal bundle method for convex minimization in Hilbert spaces. 
Optimization 65, 145--167 (2016).  
(MATLAB_codes).  PDF  |  doi>

J.Y. Bello CruzA.N. Iusem. 
Full convergence of an approximate projection method for nonsmooth variational inequalities. 
Mathematics and Computers in Simulation.  114, 2--13 (2015). 
 PDF  |  doi>

J.Y. Bello CruzR. Díaz Millán
A variant of forward-backward splitting method for the sum of two monotone operators with a new search strategy. 
Optimization64, 1471--1486 (2015).  
 PDF  |  doi>

J.Y. Bello Cruz, G. Bouza Allende. 
A steepest descent-like method for variable order vector optimization problems. 
Journal of Optimization Theory and Application. 162, 371--391 (2014). 
 PDF  |  doi>

J.Y. Bello Cruz, G. Bouza AllendeL.R. Lucambio Pérez
Subgradient algorithms for solving variable inequalities.
Applied Mathematics and Computation247, 1052--1063 (2014). 
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The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle. 
Journal of Approximation Theory.  185, 63--79 (2014). 
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J.Y. Bello CruzR. Díaz Millán
A direct splitting method for nonsmooth variational inequalities. 
Journal of Optimization Theory and Application161, 728--737 (2014). 
 PDF  |  doi>

J.Y. Bello CruzW. de Oliveira. 
Level bundle-like algorithms for convex optimization.
Journal of Global Optimization. 59, 787--809 (2014).  
(MATLAB_codes).  PDF  |  doi>

J.Y. Bello CruzL.R. Lucambio Pérez. 
A subgradient-like algorithm for solving vector convex inequalities. 
Journal of Optimization Theory and Application.  162, 392--404 (2014). 
 PDF  |  doi>

J.Y. Bello Cruz.
A subgradient method for vector optimization problems. 
SIAM Journal on Optimization. 23, 2169--2182 (2013). 
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J.Y. Bello Cruz, S. Scheimberg, P.S.M. Santos. 
A two-phase algorithm for a variational inequality formulation of equilibrium problems. 
Journal of Optimization Theory and Application. 159, 562--575 (2013). 
 PDF  |  doi>

J.Y. Bello CruzA.N. Iusem. 
An explicit algorithm for monotone variational inequalities. 
Optimization. 61, 855--871 (2012). 
 PDF  |  doi>

J.Y. Bello CruzL.R. Lucambio Pérez, J.G. Melo. 
Convergence of the projected gradient method for quasiconvex multiobjective optimization. 
Nonlinear Analysis74, 5268--5273 (2011). 
 PDF  |  doi>

J.Y. Bello CruzA.N. Iusem. 
A strongly convergent method for nonsmooth convex minimization in Hilbert spaces. 
Numerical Functional Analysis and Optimization. 32, 1009--1018 (2011). 
 PDF  |  doi>

J.Y. Bello CruzH. Pijeira Cabrera, C. Márquez, W. Urbina Romero
Sobolev-Gegenbauer type orthogonality and a hydrodynamical interpretation.
Integral Transforms and Special Functions. 22, 711--722 (2011). 
 PDF  |  doi>

J.Y. Bello CruzH. Pijeira Cabrera, W. Urbina Romero. 
On polar Legendre polynomials. 
Rocky Mountain Journal of Mathematics. 40, 2025--2036 (2010). 
 PDF  |  doi>

J.Y. Bello CruzA.N. Iusem. 
Convergence of direct methods for paramonotone variational inequalities. 
Computational Optimization and Applications. 46, 247--263 (2010). 
 PDF  |  doi>

J.Y. Bello Cruz L.R. Lucambio Pérez. 
Convergence of a projected gradient method variant for quasiconvex objectives. 
Nonlinear Analysis. 9, 2917--2922 (2010). 
 PDF  |  doi>

J.Y. Bello CruzA.N. Iusem. 
A strongly convergent direct method for monotone variational inequalities in Hilbert spaces. 
Numerical Functional Analysis and Optimization. 30, 23--36 (2009). 
 PDF  |  doi>

J.Y. Bello Cruz.
Direct Methods for Monotone Variational Inequalities. 
Doctoral dissertation. PREPRINT IMPA C095 / 2009. 1--93 (2009). 
(Advisor: Alfredo Iusem).  PDF  

Research Interests: Calculus of variations and optimal control; Optimization; Fourier analysis; Operations research; Mathematical programming; Operator theory

  • (2018(Ongoing) - Ph.D. Dissertation supervision of Oday Hazaimah, Department of Mathematical Sciences (DMS), Northern Illinois University (NIU), USA. Currently: Teaching assistant at DMS, NIU, USA
  • (2015 - 2016) (Interrupted) - Ph.D. Dissertation Co-supervision of P.C. Silva Junior - Currently, Ph.D. Student at Institute of Mathematics and Statistics, Federal University of Goias.
  • (2012) (Supervised) - Postdoctoral Fellow Supervision of G. Bouza Allende - Currently: Assistant Professor at Faculty of Mathematics and Computation, University of Havana.
  • (2012 - 2016) - More than 5 Master's Students supervisions at Institute of Mathematics and Statistics, Federal University of Goias; for further details (in Portuguese) see [a], [b], [c], [d], [e], etc. 

Co-authors and Collaborators from MathSciNet and Scopus

Ackooij, W.V. & Barrios, J.G. & Bauschke, H.H. & Behling, R. Bouza Allende, G. & de Oliveira, W. & Díaz Millán, R. & Ferreira, O.P. & Iusem, A.N. & Lucambio Pérez, L.R. & Márquez, C. & Melo, J.G. & Nemeth, S.Z. & Nghia, T.T.A & Pang, H.M. & Pijeira-Cabrera, H. & Prudente, L.F. & Scheimberg, S. & Santos, L.R. Santos, P.S.M. & Shehu, Y. Urbina, W.O. & Wang, X. 


               - On Forward-Backward Splitting Methods

               - Subgradient algorithms for vector optimization problems.

                - A subgradient method for vector optimization problems.
                - A strongly convergent method for nonsmooth convex minimization in Hilbert spaces.
                - A modified extragradient method for variational inequalities in Hilbert spaces.
                - A strongly convergent direct method for monotone variational inequalities in Hilbert spaces.
                 - Forcing strong convergence of Korpelevich-type algorithm in Hilbert spaces.
  • Summer School, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, BRAZIL. January 2 to February 24, 2006.
               - Primitives of Classical Orthogonal Polynomial 
  • IV Summer School (MECESUP), Centro de Modelamiento Matemático, University of Chile, Santiago de Chile, CHILE. November 29 to December 17, 2004.
  • School on Information and Randomness, Departamento de Ingeniería Matemática y Centro de Modelamiento Matemático, University of Chile, Santiago de Chile, CHILE. December 13 - 17, 2004.
                 - On Polar Legendre Polynomials

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