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Associate Professor Regina Burachik
Position: Associate Professor Associate Professor Regina Burachik
Division/Portfolio: Division of Information Technology, Engineering and the Environment
School/Unit: School of Mathematics and Statistics
Campus: Mawson Lakes Campus
Office: OC1-36
Telephone: +61 8 830 25537
Fax:
Email: Regina_dot_Burachik_at_unisa_dot_edu_dot_au
URL for Business Card: http://people.unisa.edu.au/Regina.Burachik

Welcome to my homepage!

 

Research Interests

  • Optimization
  • Convex Analysis
  • Non-smooth Analysis
  • Set-Valued Analysis
  • Variational Inequalities
  • Proximal-like Methods

Scroll down to see a list of my publications and links to most articles

Teaching

 

 

2009

Study Period 2 (formerly, Semester 1)

 

 

 

 

 

Study Period 5 (formerly, Semester 2)

 

 

 

 

2008

Study Period 2 (formerly, Semester 1)

 

 

 

Study Period 5 (formerly, Semester 2)

 

 

 

2007

 

 

Study Period 2

 

 

2006 and Before

 

 

 

  • Optimisation (UniSA, 2003)
  • Differential Equations (UniSA, 2005, 2006)
  • Convex Analysis (Federal University of Rio de Janeiro - UFRJ)
  • Numerical Analysis (UFRJ)
  • Nonlinear Programming (UFRJ)
  • Interior Point Methods for Linear Programming (UFRJ)
  • Duality Theory in Convex Programming (UFRJ)
  • Newton's Method and Its Variants  (UFRJ)
  • Primal-Dual Methods for Linear Programming  (UFRJ)
  • Numerical Linear Algebra  (UFRJ)


Link to the Honours course Advanced Optimization.

My Google Scholar search hits.

Teaching interests

  • Convex Analysis.
  • Optimization, smooth and non-smooth.
  • Set-valued Analysis
  • Differential Equations and applications
  • Numerical Analysis

I teach the following courses

MATH 1054Calculus 1
MATH 2002Differential Equations
MATH 1005Honours Mathematical Studies 2
MATH 1039Mathematics for Laboratory Sciences 100
MATH 3026Applied Functional Analysis
MATH 3010Advanced Operations Research

Professional associations

Member of Editorial Board of the Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM Journal)

Member of Editorial Board of Applied Mathematics and Computation

Member of Editorial Board of Communications in Mathematical Analysis

Member of the Australian Mathematical Society

Qualifications

PhD in Mathematics,
Instituto de Matemática Pura e Aplicada
Institute of Pure and Applied Mathematics -IMPA
Rio de Janeiro, March 1995.
Title of the Thesis: Generalized Proximal Point Method for the Variational Inequality Problem
(it produced the works [5] and [9] in the list of Publications below).
Citations to Thesis in Google Scholar by 31/8/2009: 20
Click here for up-to-date citations in Google Scholar

MSc in Pure Mathematics,
Licenciatura en Matemática Pura
Facultad de Ciencias Exactas y Naturales
Universidad de Buenos Aires, 1987.

Research interests

  • Optimization (Smooth and Nonsmooth)
  • Convex Analysis
  • Non-smooth Analysis
  • Set-Valued Analysis
  • Proximal-like Methods
  • Variational Inequalities

Research publications

Updated on 23 October 2009.
Please contact me by email for a copy of my publications. Technical report versions
can be downloaded by clicking on the titles, if a link is provided. Corrections,
suggestions and comments on these publications are always welcome. Please let me
know if a link is not working properly.
Citation Numbers for Journal articles from ISI Web of Science, cited reference search by 23/10/2009.

 

Book
 

[B1] Burachik, R. S., Iusem, A. N.
Set-Valued Mappings and Enlargements of Monotone Operators,

Springer Optimization and Its Applications, Vol 8, 300 pp. Hardcover, ISBN: 978-0-387-69755-0, 2008.

[Contents]  [MathSciNet Review] [ZentralBlatt Review]

Times cited by 31/08/2009 - Google scholar: 16
Click here for up-to-date citations in Google Scholar

New Page 1

Edited Volumes
 

[EV1] Guest Editors: Burachik, R. S., Fliege, J., and Kocvara, M.
Special issue, Part I: the Joint EUROPT-OMS Conference on Optimization
July 4-7, 2007, Prague, Czech Republic.
Optimization Methods and Software, 23:(5), 2008.

[EV2] Guest Editors: Burachik, R. S., and Yang, X. Q.
Special issue dedicated to the memory of Prof. Dr Alexander Moiseevich Rubinov.
Optimization, 56:(5-6), 2007.

New Page 1

Journal Publications
 

2009

[36] Burachik, R. S.; Iusem, A. N.; Melo, J. G.
A Primal Dual Modified Subgradient Algorithm with Sharp Lagrangian
Journal of Global Optimization, (to appear)

[35] Burachik, R. S.; Lopes, J. O., Da Silva, G. J. P.
An inexact interior point method for the variational inequality problem.
Computational & Applied Mathematics, (28)1:1-22, 2009.

2008

[34] Burachik, R. S. and Lopes, J. O.
Outer approximation schemes for generalized semi-infinite variational inequality problems
Optimization
Published Online: 14 August 2008, DOI: 10.1080/02331930801956552.

[33] Burachik, R. S., Kaya, C. Y., and Mammadov, M.
An inexact modified subgradient algorithm for nonconvex optimization.
Computational Optimization and Applications
Published online: 29 Jan 2008, DOI: 10.1007/s10589-008-9168-7.

[32] Burachik, R. S.; Rubinov, A.
On abstract convexity and set valued analysis.
Journal of Nonlinear and Convex Analysis, (9)1:105-123, 2008.

[31] Burachik, R. S., Grana Drummond, L. and Scheimberg, S.
On some properties and an application of the logarithmic barrier method
Mathematical Programming, Ser. B 111:95–112, 2008.

2007

[30] Burachik, R. S. and Kaya, C. Y.
An update rule and a convergence result for a penalty function method.
Journal of Industrial Management and Optimization 3(2): 381-398, 2007.
Times cited: 1

[29] Burachik, R. S. and Rubinov, A.
Abstract Convexity and Augmented Lagrangians.
SIAM Journal on Optimization vol. 18, 413-436, 2007.
Times cited: 2

2006

[28] Burachik, R. S. and Svaiter, B.F.
Operating enlargements of monotone operators.
Pacific Journal of Optimization 2(3): 425-445, 2006.
Times cited: 1

[27] Burachik, R. S. and Iusem, A.N.
On enlargeable and non-enlargeable maximal monotone operators.
Journal of Convex Analysis, 13(3/4): 603-622, 2006.
Times cited: 2

[26] Burachik, R. S., Jeyakumar, V. and Wu, Z.Y.
 Necessary and sufficient conditions for stable conjugate duality.
Journal of Nonlinear Analysis, 64: 1998--2006, 2006.
Times cited: 12

[25] Burachik, R. S., Sagastizabal, C. A. and Scheimberg, S.
An inexact method of partial inverses: Application to splitting methods.
Optimization Methods and Software, 21(3): 385--400, 2006.

[24] Burachik, R. S., Gasimov, R., Ismayilova, N. and Kaya, C.Y.
On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian.
Journal of Global Optimization, 34(1): 55--78, 2006.
Times cited: 4

2005

[23] Burachik, R. S. and Jeyakumar, V.
A dual condition for the convex subdifferential sum formula with Applications.
Journal of Convex Analysis, 12(2): 279-290, 2005.
Times cited: 22

[22] Burachik, R. S., Lopes, J.O. and Svaiter, B.F.
An outer approximation method for the variational inequality problem.
SIAM Journal on Control and Optimization,43(6): 2071--2088, 2005.
Times cited: 8

[21] Burachik, R. S.and Fitzpatrick, S.
On the Fitzpatrick family associated to some subdifferentials.
Journal of Nonlinear and Convex Analysis, 6(1):165--171, 2005.
Times cited: 6

[20] Burachik, R. S. and Jeyakumar, V.
A simple closure condition for the normal cone intersection formula.
Proceedings of the American Mathematical Society. 133(6): 1741--1748, 2005.
Times cited: 14

[19] Burachik, R. S. and Jeyakumar, V.
 A new geometric condition for Fenchel duality in infinite dimensions.
Mathematical Programming, 104(2-3)(B), 229--233, 2005.
Times cited: 12

[18] Burachik, R. S. and Rubinov, A.
On the absence of duality gap for a family of Lagrange-type functions.
Journal of Industrial Management and Optimization, 1(1):33--38, 2005.
Times cited: 4

2003

[17] Burachik, R. S.; Svaiter, B.F.,
Maximal monotonicity, conjugation and the duality product.
Proceedings of the American Mathematical Society, 131(8): 2379--2383, 2003.
Times cited: 15

[16] Burachik, R. S.; Lopes,J. O.
A convergence result for an outer approximation scheme.
Computational & Applied Mathematics, 22(3): 397--409, 2003.

[15] Burachik, R. S.; Scheimberg,Susana; Silva,Paulo J.S.
 A note on the existence of zeroes of convexly regularized sums of maximal monotone operators.
Journal of Mathematical Analysis and Applications, 280(2): 313--320, 2003.

2002

[14] Burachik,R. S.; Svaiter,B.F.
 Maximal monotone operators, convex functions and a special family of enlargements.
Set Valued Analysis, 10(4): 297--316, 2002.
Times cited: 22

2001

[13] Burachik, R. S.; Scheimberg,S.; Svaiter,B.F.
Robustness of the hybrid extragradient proximal-point algorithm.
Journal of Optimization Theory and Applications, 111(1): 117--136, 2001.
Times cited: 5

[12] Burachik, R. S.; Svaiter,B.F.
 A relative error tolerance for a family of generalized proximal point methods.
Mathematics of Operations Research, 26(4): 816--831, 2001.
Times cited: 9

[11] Burachik, R. S.; Scheimberg,S.,
A proximal point method for the variational inequality problem in Banach spaces.
SIAM Journal on Control and Optimization, 39(5): 1633--1649, 2001.
Times cited: 22

2000

[10] Burachik, R. S.; Butnariu,D.; Iusem, A. N.
Iterative methods for solving stochastic convex feasibility problems and applications,
Computational Optimization and Applications, 15(3): 269--307, 2000.
Times cited: 10

1999

[9] Burachik, R. S.; Iusem, A. N.
A generalized proximal point algorithm for the nonlinear complementarity problem.
RAIRO-Operations Research, 33(4): 447--479, 1999.

[8] Burachik, R. S.; Sagastizábal,C. A.; Svaiter,B.F.
Epsilon-enlargements of maximal monotone operators: Theory and applications.
Applied Mathematics and Optimization, 22: 25--43, 1999.
Times cited: 27

[7] Burachik, R. S.; Svaiter, B.F.
Epsilon-enlargements of maximal monotone operators in Banach spaces.
Set-Valued Analysis, 7(2):117-–132, 1999.
Times cited: 27

[6] Burachik, R. S., Sagastizabal, C.; Svaiter, B.F.
Bundle methods for maximal monotone operators.
Lecture Notes in Economy and Mathematical Systems, 477: 49--64, 1999.
Times cited: 13

1998

[5] Burachik, R. S.; Iusem, A. N.
A generalized proximal point algorithm for the variational inequality problem in a Hilbert space.
SIAM Journal on Optimization, 8(1): 197-–216, 1998.
Times cited: 49

1997

[4] Alber, Y., Burachik, R. S., Iusem, A.
A proximal point method for nonsmooth convex optimization problems in Banach spaces.
Abstract and Applied Analysis, 2(1-2): 97-–120, 1997.

New Page 1

[3] Burachik, R. S., Iusem, A. N.; Svaiter, B.F.
Enlargement of monotone operators with applications to variational inequalities.
Set-Valued Analysis, 5(2): 159-–180, 1997.
Times cited: 63

1995 or earlier

[2] Burachik, R. S., Grana Drummond, L., Iusem, A. N.; Svaiter, B.F.
Full convergence of the steepest descent method with inexact line searches.
Optimization, 32(2): 137–-146, 1995.
Times cited: 18

[1] Burachik, R. S.; Maestripieri, A.
On the principal eigenvalue of a Neumann problem with weight.
Revista de la Union Matematica Argentina, 36: 174-–180, 1990.

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Expertise for Media Contact

I am able to provide media comment in the following areas of expertise:

Discipline: Applied Mathematics

  • Optimization
  • Convex Analysis
  • Functional Analysis
  • Set-Valued Analysis



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