"What we think, we become"
Last Updated by November 2017

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

About Me: My main research interest is in the area of Continuous Optimization, focusing on Nonsmooth and Convex Optimization, Variational Inequalities, Inclusion Problems, Algorithms, and Applications. I did my Ph.D. in Mathematics under the supervision of Prof. Alfredo Iusem at the Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil. After my Ph.D., I worked with Prof. Heinz Bauschke as a CNPq Postdoctoral Research Fellow in the Irving K. Barber School of Arts and Sciences, Mathematics at the University of British Columbia, Canada. From 2009 to 2016, I was Assistant Professor in the Institute of Mathematics and Statistics at the Federal University of Goias, Brazil. Currently, I work in the Department of Mathematical Sciences at Northern Illinois University as an Assistant Professor in Numerical Analysis and Optimization. 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 

Citizenship: CUBAN (Permanent Resident in BRAZIL



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

R. BehlingJ.Y. Bello-CruzL. R. Santos.
On linear convergence of the circumcentered--reflexion method. (Submitted 2017) 
.BIB  |  PDF 

J.Y. Bello Cruz, G. LiT.T.A. Nghia
On the Q-linear convergence of the forward-backward splitting method and uniqueness of optimal solution to Lasso. (Submitted 2017) 
.BIB  |  PDF 

J.Y. Bello Cruz, G. Bouza Allende. 
Inexact projected gradient methods for vector optimization problems on variable ordered spaces. (Submitted 2017
.BIB  |  PDF   

J.Y. Bello CruzR. Díaz MillánH.M. Phan
Conditional extragradient algorithms for variational inequalities. (Submitted 2016) 
.BIB  |  PDF 

R. BehlingJ.Y. Bello CruzL. R. Santos
Circumcentering the Douglas--Rachford method. 
Numerical Algorithms. pp. 1--18. DOI: 10.1007/s11075-017-0399-5 -- to appear (2018).  
.BIB  |  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).  
.BIB  |  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). 
.BIB  |  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). .BIB  |  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). 
.BIB  |  PDF  |  doi>

Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces. 
Numerical Algorithms. 73, 33--76 (2016). 
.BIB  |  PDF  |  doi>

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).  .BIB  |  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)
.BIB  |  PDF  |  doi>

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).  .BIB  |  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).  
.BIB  |  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). .BIB  |  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). 
.BIB  |  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).  
.BIB  |  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). 
.BIB  |  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). 
.BIB  |  PDF  |  doi>

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). 
.BIB  |  PDF  |  doi>

J.Y. Bello CruzR. Díaz Millán
A direct splitting method for nonsmooth variational inequalities. 
Journal of Optimization Theory and Application161, 728--737 (2014). 
.BIB  |  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). .BIB  |  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). 
.BIB  |  PDF  |  doi>

J.Y. Bello Cruz.
A subgradient method for vector optimization problems. 
SIAM Journal on Optimization. 23, 2169--2182 (2013). 
.BIB  |  PDF  |  doi>

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). 
.BIB  |  PDF  |  doi>

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

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

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

  • (2015 - present) - 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) - 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 see [a], [b], [c], [d], [e], etc. 

Co-authors and Collaborators from MathSciNet and Scopus

Ackooij, W.V. & Barrios, J.G. & Bauschke, H.H. & 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, P.S.M. & Urbina, W.O. & Wang, X. 


  • Supported by CAPESInternational Symposium on Mathematical Programming, Pittsburgh, July - PA, USA.
  • (R$ 36,000) 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. Federal University of Goiás. 2013 - 2014.
  • (R$ 125,000) Project CAPES/MES-CUBA. "Modelos de Otimização e Aplicações". Sponsorship by CAPES. Federal University of Goiás. 2012 - 2016.
  • 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.  
  • Grant funds from CAPES for 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.
  • 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.


               - 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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