Dr. Nataša Krejić

Curriculum Vitae

Personal Data

Languages

·        Mother tongue: Serbian

·        Foreign languages: English, Portuguese

Education

B.S., Faculty of Science, Novi Sad, Yugoslavia, 1985-1989.

M.S., Faculty of Science, Novi Sad, Yugoslavia, 1992.

Ph. D., Faculty of Science, Novi Sad, Yugoslavia, 1994.

Experience

Visiting Professor, Institute of Mathematics, University of Campinas, SP, Brazil, 2011 (6 weeks), grant from FAPESP, SP

Erasmus Mundus Visitor, Technical University of Eindhoven, Holland, 2009

Senior Research Fellowship, CEU, Budapest, Hungary, 2009

Visiting Professor, Institute of Mathematics, University of Campinas, SP, Brazil, 2003 (1 month), grant from FAPESP, SP

Visiting Professor, Institute of Mathematics, University of Campinas, SP, Brazil, 1999-2000 (15 months), grant from FAPESP, SP

Visiting Professor, Institute of Mathematics, University of Campinas,  SP, Brazil,  1997 (6 months), grant from FAPESP, SP

Full Professor, Faculty of Science, University of Novi Sad, 2004-.

Associate Professor, Faculty of Science, University of Novi Sad, 1999 –2004.

Assistant Professor, Faculty of Science, University of Novi Sad, 1995-1999.

Assistant, Faculty of Science, University of Novi Sad, 1990-1995.

Publications

  1. Krejić, N., Krklec, N., Line search methods with variable sample size for unconstrained optimization, technical report

  2. Krejić, N., Lužanin, Z., Ovcin, Z., Stochastic Newton-like methods for computing equilibria in general equilibrium models, Computational and Applied Mathematics, vol. 30, no.1 (2011), 127-149. download

  3. E. G. Birgin, L. F. Bueno, N. Krejić, J. M. Martinez,  Low Order-Value Optimization approach for solving VaR-constrained minimization problems, Journal of Global Optimization 51,4 (2011), 715-742. technical report

  4. Krejić, N., Lužanin, Z., Stojkovska I., Gradient type method for optimization in noisy environment, technical report

  5. Krejić, N., Kumaresan, M., Rožnjik, A., VaR optimal portfolio with transaction costs, Applied Mathematics and Computation, 218, 8, (2011), 4626-4637, technical report

  6. Kumaresan, M., Krejić, N., A Model for Optimal Execution of Atomic Orders, Computational Optimization and Applications 46,2, 369-389, 2010 technicalreport

  7. Ćurić, V., Heilio, M., Krejić, N., Nedeljkov, M., Mathematical Model for Efficient Water Flow Management, Nonlinear Analysis: Real World Applications 11 (2010) 1600-1612 chknr1.pdf

  8. Krejić, N., Lužanin, Z., Ovcin, Z., Hybrid stochastic optimization algorithms with line search, submitted.  download

  9. Krejić, N., Lužanin, Z., Stojkovska, I., Gauss-Newton-based BFGS method with filter for unconstrained optimization, Applied Mathematics and Computation 211,1, (2009), 354-362. download

  10. Krejić, N.,  Krunić, T., Nedeljkov, M., Numerical verification of delta shock waves for pressureless gas dynamics, Journal of Mathematical Analysis and Applications, Volume 345, Issue 1, (2008),  243-257, download

  11. Krejić, N., Lužanin Z., Rapajić, S., Jacobian smoothing Brown’s method for NCP, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 642-657.  download

  12. Buhmiler, S., Krejić, N., Lužanin, Z., Practical Quasi-Newton methods for singular nonlinear systems, Numerical Algorithms (to appear) download

  13. Krejić, N., Rapajić, S., Globally convergent Jacobian smoothing inexact Newton methods for NCP, Computational Optimization and Applications, Volume 41, Number 2 (2008), 243-261.

  14. Krejić, N., Lužanin, Z., Radeka, I., Newton-like method for nonlinear banded block diagonal system , Applied Mathematics and Computation, Volume 189, Issue 2,  (2007), 1705-1711.

  15. Buhmiler, S., Krejić, N, A new smoothing quasi-Newton method for nonlinear complementarity problems, Journal of Computational and Applied Mathematics vol 211, No 2, (2008), 141-155.

  16. Krejić; N.,  Lužanin, Z., Rapajić, S., Iterative method with modification of the right-hand side vector for nonlinear complementarity problems, Internat. J. Comput. Math. 83, 2(2006), 193-201.

  17. Francisco, J.B., Krejić, N., Martínez, J.M, An interior-point method for solving box-constrained underdetermined nonlinear systems, Journal of Computational and Applied Mathematics 177,1 (2005), 67-88.

  18. Birgin, E.G., Krejić, N., Martínez, J.M., Solution of bounded nonlinear systems of equations using homotopies with inexact restoration, Internat. J. Comput. Math. 80(2): 211-222 (2003).

  19. Birgin, E.G., Krejić, N., Martínez, J.M., Globally convergent inexact quasi – Newton methods for solving nonlinear systems, Numerical Algorithms 32 (2003), 249-260.

  20. Krejić, N., Lužanin, Z., Newton-like method with modification of the right-hand side vector Mathematics of Computation,  71, 237 (2002), 237-250.

  21. Krejić, N., Rapajić, S., Lužanin, Z.,  On a Smoothing Quasi-Newton Method for Nonlinear Complementarity Problems, GAMM 2003, 24-28. 3. 2003, Abano Terme, Padua, Italy, PAMM - Proc. Appl. Math. Mech., Vol. 3, Issue 1,

  22. Herceg, D., Krejić, N., Maličić, H., On an iterative method with deflation for systems of equations, Novi Sad J. Math., 29,1 (1999), 169-175.

  23. Herceg, D., Krejić, N., Maličić, H., On a finite difference analogue of a singularly boundary value problem,  Novi Sad J. Math., 31,1 (2000), 23-31.

  24. Krejić, N., Rapajić, S., Quasi-Newton methods for semi-smooth reducible systems, XIII Conference on Applied Mathematics, D. Herceg, K. Surla, N. Krejić, eds., Institute of Mathematics, Novi Sad, 2000, pp. 63-74

  25. Krejić, N., Lužanin, Z.,  Relaxation of Quasi-Newton method, XII Conference on Applied Mathematics, Herceg, D., Surla, K., eds., Institute of Mathematics, Novi Sad, 1998.

  26. Krejić, N., Martínez, J.M., Mello, M., Pilotta, E.A., Validation of an Augmented Lagrangian Algorithm with a Gauss-Newton Hessian Approximation Using a Set of Hard-Spheres Problems, Computational Optimization and Applications 16 (2000), 247-263.

  27. Krejić, N., Martínez, J.M., Inexact Newton methods for semismooth systems of equations with block-angular structure, Journal of Computational and Applied Mathematics 103, (1999), 239-249.

  28. Krejić, N., Martínez, J.M., A globally convergent Inexact-Newton method for solving reducible systems of equations, Optimization Methods and Software 13 (2000), 11-34.

  29. Krejić, N., Lopes, V., Martínez, J.M., Peres, R., Globally convergent incomplete decomposition algorithms for discrete dynamic nonlinear models, Nonlinear Analysis 42 (2000), 663-672.

  30. Herceg, D., Krejić, N., Lužanin, Z., Quasi-Newton method with correction, Novi Sad J. Math., 26,1 (1996), 115-127.

  31. Herceg, D., Krejić, N., Hybrid methods for solving discrete analogues of nonlinear boundary value problems, Nonlinear Analysis, 30 (1997), 9-15.

  32. Lužanin, Z., Herceg, D., Krejić, N., Parameter selection for inexact Newton methods, Nonlinear Analysis 30 (1997), 17-24.

  33. Herceg, D., Krejić, N., On an acceleration of iterative methods for discrete analogues of SPP boundary value problems, XI Conference on Applied Mathematics, D. Herceg, K. Surla, eds., Institute of Mathematics, Novi Sad, 1997, 91-101.

  34. Herceg, Đ., Krejić, N., Computation of coefficients of difference formulas on an arbitrary mesh. Proceedings of the VII Conference on Logic and Computer Science Lira '95, Novi Sad, September 26-30, pp. 45-51.

  35. Herceg, D., Krejić, N., On the strong componentwise stability and H-matrices, Demonstratio Mathematica 30,2 (1997), 373-378.

  36. Herceg, D., Krejić, N., Convergence results for fixed point iterations in R, Computers Math. Applic. 31,2 (1996), 7-10.

  37. Herceg, D., Krejić, N., On a modification of iterative methods, X Conference on Applied Mathematics, Herceg, D., Cvetković, Lj., eds., Institute of Mathematics, Novi Sad, 1996, 9-17.

  38. Krejić, N., Extension of convergence area and convergence acceleration for twoparametric relaxation methods, Ph.D. thesis, University of Novi Sad, Institute of Mathematics, Novi Sad, 1994, 97 pgs. (in Serbian).

  39. Herceg, D., Krejić, N., Fixed point iterations in R , IX Conference on Applied Mathematics, Herceg, D., Cvetković, Lj., eds., Institute of Mathematics, Novi Sad, 1995, 21-27.

  40. Krejić, N., Ogrizović, Z., Nonlinear AOR method, IX Conference on Applied Mathematics, Herceg, D., Cvetković, Lj., eds., Institute of Mathematics, Novi Sad, 1995, 55-63.

  41. Herceg, D., Krejić, N., Extensions of the Convergence Area for the AOR Method with Gaussian Elimination, Proc. Lucrarile Sesuinii de Comunicari Stiintifice, Halic, G., ed. Arad, 1994, 1-7.

  42. Krejić, N., Herceg, D., Improving the convergence of iterative methods by performing Gaussian elimination, VIII Conference on Applied Mathematics, Jaćimović, M., ed., Tivat 1993, 103-110.

  43. Herceg, D., Krejić, N., Some properties of matrices arising from the discretization of boundary value problems, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat- Fak- Ser. Mat. 24,1 (1994), 379-389.

  44. Herceg, D., Krejić, N., Column Relaxation and Hybrid Acceleration, Z. angew. Math. Mech., 74(6), 673-675.

  45. Cvetković, Lj., Krejić, N., USSOR Method for SDD matrices, Z. angew. Math. Mech. 74(6), 673-675.

  46. Cvetković, Lj., Krejić, N., Local and global convergence of the nonlinear USSOR method , Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23,2 (1993), 381-391.

  47. Herceg, D., Krejić, N., On the Convergence of the Unsymmetric Succesive Overrelaxation (USSOR) Method, Linear Algebra Appl. 185 (1993), 49-60

  48. Cvetković, Lj., Krejić, N., Convergence of the Unsymmetric Succesive Overrelaxation Method for the SDD matrices, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22,2 (1992), 11-21.

  49. Krejić, N., Some techniques for the Acceleration of Iterative Methods, Master Thesis, Faculty of Science, University of Novi Sad, 1992, 75 pgs (in Serbian).

  50. Herceg, D., Krejić, N., A Remark on Iterative Methods for Systems of Linear Equations,  Bull. Appl. Math. 779 (1992)(LXI), 29-37.

  51. Herceg, D., Krejić, N., On a Hybrid Methods for a System of Linear Equations, Bull. Appl. Math. 704 (1991)(LVII), 29-37.

  52. Herceg, D., Krejić, N., On a Nonstationary Modification of an Iterative Method, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat.Fak. Ser. Mat. 22,2 (1992), 1-10.

  53. Herceg, D., Krejić, N., On Two Relaxation Methods for Solving Systems of Nonlinear Equations, VII Conference on Applied Mathematics, R. Scitovski, ed., University of Osijek, Osijek, 1990, 79-89.

 

Books in Serbian

1.     Krejić, N., Herceg, Đ., Mathematics and Mathematica, University of Novi Sad, Institute of Mathematics, 1993, 177pgs., second edition 1994, xi+186 pgs., third edition 1997, 200 pgs, fourth edition, 2001, fifth edition 2007

2.     Herceg, D., Krejić, N., Numerical Analysis, University of Novi Sad, Stylos, Novi Sad, 1997, 397 pgs.

3.     Herceg, D., Krejić, N., Numerical Analysis – Collection of Solved Problems I, University of Novi Sad, Novi Sad, 1998, 231 pgs.

4.     Herceg, D., Krejić, N., Numerical Analysis – Collection of Solved Problems II, University of Novi Sad, Novi Sad, 1998, 187 pgs.

5.     Gajić, Lj., Herceg, D., Krejić, N., Elements of Business Mathematics, Institute of Mathematics, Novi Sad, 1999, 200 pgs, , second edition 2000, third edition 2001..

6.     Herceg, D., Krejić, N., Numerical Analysis for Computer Science Students, University of Novi Sad, Tempus SCM project, Novi Sad, 2005

Project Leadership

Project Coordinator: Tempus JEP CD 17017-2002: Mathematics Curricula for Technological Development, 2003-2006, financed by EC

Numerical Methods for Nonlinear Mathematical Models, Serbian Ministry of Science and Enviromental Protection, grant 144016, 2006-2010

Numerical Methods, Simulations and Applications, Ministry of Science and Technological Development, REpublic of Serbia, no. 174030, 2011-2014.

Modelling and Forecasting Stock Price Behaviour – Analysis of High Frequency Financial Data – Research project for Dresdner Kleinwort Securities, London, 2006-2007.

Teaching

Courses:at Master programme of Applied Mathematics at University of Novi Sad:  Financial Mathematics , Numerical Optimization, Numerical Analysis

Course on Portfolio Optimization at Lappeenranta University of Technology, Finland, May 2006.

PhD and MSc Students

Miles Kumaresan, Optimization of Conditional Trajectories in a Market Place of Multiple Liquidity Pools, PhD thesis, University of Novi Sad, Faculty of Science, 2010, download

Sanja Rapajić, Smoothing Iterative Methods for Nonlinear Complementarity Problems, PhD thesis, University of Novi Sad, Faculty of Science, 2005.

Milena Kresoja, Scenario Generation with Hidden Markov Models, M Sc thesis, University of Novi Sad, Faculty of Science, 2011, download

Svetlana Milovanović, Stability of the Covariance Matrix and Portfolio Optimization Problem, M Sc thesis, University of Novi Sad, Faculty of Science, 2011, download

Sonja Rauški, Pоrtfolio Optimization with Uncertain Exit Time, M Sc thesis, University of Novi Sad, Faculty of Science, 2011, download

Ivana Manić, Mathematical Methods for Measuring and Managing Operational Risk, M Sc thesis, University of Novi Sad, Faculty of Science, 2008, download

Vojislav Timarac, Smoothing methods for linear programming problems, M Sc thesis, University of Novi Sad, Faculty of Science, 2008.

Nataša Teodorović, Liquidity measures and price impact function, M Sc thesis, University of Novi Sad, Faculty of Science, 2008. download

Andrea Rožnjik, VaR as a risk measure in portfolio optimization,  M Sc thesis, University of Novi Sad, Faculty of Science, 2008. download

Katarina Vla, Optimization of credit portfolio with CVaR, M Sc thesis, University of Novi Sad, Faculty of Science, 2007. download

Dragan Kovačević, Mathematical models of Stock Exchange Trading, M Sc thesis, University of Novi Sad, Faculty of Science, 2007.

Sandra Buhmiler, Quasi-Newton Methods for Nonlinear Complementarity Problems, M Sc thesis, University of Novi Sad, Faculty of Science, 2005

Tanja Nedić, Adaptive Grids for Delta Waves, MSc thesis, University of Novi Sad, Faculty of Science, 2003