Regina Burachik

Research Interests

Operator Algebras and Functional Analysis Optimisation

Teaching Strengths

Optimisation
Functional Analysis
Calculus at all levels
Linear Algebra
Numerical Linear Algebra

Prof Regina Burachik

School of Mathematical Sciences

College of Science

Eligible to supervise Masters and PhD - email supervisor to discuss availability.

Available For Media Comment.

I am a Professor of Mathematics at STEM-UniSA.
My research focuses on several aspects of optimization, ranging from functional analysis and variational inequalities to practical applications. I publish in optimization theory, solution techniques for nonsmooth optimization, and convergence analysis of algorithms. My interests span 

theoretical aspects of optimization,
constraint qualifications for nonsmooth optimization,
theory of monotone operators,
convex analysis,
multiobjective optimization and the development of new scalarization techniques.

I have published more than 70 journal articles in these topics and co-authored a Springer book entitled "Set-valued Analysis and enlargements of monotone operators", which focuses on the use of point-to-set theory for optimization. I am an associate editor of several international journals in the field of optimization.

Date Position Institution name
2020 - 2022 Professor University of South Australia

Date Institution name Country Title
1991 - 1995 Centro di Ricerca in Matematica Pura ed Applicata Brazil PhD in Mathematics

Year Citation
2025 Burachik, R. S., & Martinez Legaz, J. E. (2025). Note on Carlier's inequality. Optimization, online, 1-7.
DOI
2024 Burachik, R. S., Caldwell, B. I., Kaya, C. Y., & Moursi, W. M. (2024). Optimal control duality and the Douglas-Rachford algorithm. SIAM Journal on Control and Optimization, 62(1), 680-698.
DOI
2024 Burachik, R. S., Caldwell, B. I., & Kaya, C. Y. (2024). Douglas-Rachford algorithm for control- and state-constrained optimal control problems. AIMS Mathematics, 9(6), 13874-13893.
DOI
2024 Burachik, R. S., Kaya, C. Y., & Moursi, W. M. (2024). Infeasible and critically feasible optimal control. Journal of Optimization Theory and Applications, 203(2), 1219-1245.
DOI
2024 Burachik, R. S., Caldwell, B. I., & Kaya, C. Y. (2024). Douglas-Rachford algorithm for control-constrained minimum-energy control problems. ESAIM: Control, Optimisation and Calculus of Variations, 30(18), 1-33.
DOI
2024 Bui, H. T., Burachik, R. S., Nurminski, E. A., & Tam, M. K. (2024). Single-projection procedure for infinite dimensional convex optimization problems. SIAM Journal on Optimization, 34(2), 1646-1678.
DOI Scopus2
2023 Burachik, R. S., Kaya, C. Y., & Liu, X. (2023). A primal-dual algorithm as applied to optimal control problems. Pure and Applied Functional Analysis, 8(5), 1301-1331.
DOI Scopus1
2023 Burachik, R. S., Efatmaneshnik, M., Kalloniatis, A. C., & Kaya, C. Y. (2023). Optimal organizations across many faces of complexity: synchronized networks with load-balance and minimum complexity. IEEE Systems Journal, 17(4), 5393-5404.
DOI
2022 Burachik, R. S., Hu, Y., & Yang, X. (2022). Interior quasi-subgradient method with non-Euclidean distances for constrained quasi-convex optimization problems in hilbert spaces. Journal of Global Optimization, 83(2), 249-271.
DOI Scopus2
2022 Bagirov, A. M., Burachik, R. S., Kruger, A. Y., Martinez Legaz, J. E., & Yang, X. Q. (2022). Special issue dedicated to the 80th birthday of Professor Alexander Rubinov. Optimization, 71(4), 775-778.
DOI
2022 Burachik, R., Sagastizábal, C., Stein, O., & Théra, M. (2022). Preface to the special issue geometry, optimization, and convex analysis. Set-Valued and Variational Analysis, 30(4), 1247-1249.
DOI
2022 Bui, H. T., Burachik, R. S., Kruger, A. Y., & Yost, D. T. (2022). Zero duality gap conditions via abstract convexity. Optimization, 71(4), 811-847.
DOI Scopus10
2022 Burachik, R. S., Kaya, C. Y., & Rizvi, M. M. (2022). Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems. Engineering Optimization, 54(8), 1413-4125.
DOI
2022 Burachik, R. S., Kaya, C. Y., & Price, C. J. (2022). A primal-dual penalty method via rounded weighted-ℓ1 Lagrangian duality. Optimization, 71(13), 3981-4017.
DOI Scopus7 WoS4
2021 Burachik, R. S., & Kaya, C. Y. (2021). Steklov convexification and a trajectory method for global optimization of multivariate quartic polynomials. Mathematical Programming, 189(1-2), 187-216.
DOI
2021 Burachik, R., Mordukhovich, B. S., Reich, S., & Zaslavski, A. J. (2021). Preface: optimization theory. Pure and Applied Functional Analysis, 6(6), i-ii.
2021 Burachik, R. S., Kalloniatis, A. C., & Kaya, C. Y. (2021). Sparse network optimization for synchronization. Journal of Optimization Theory and Applications, 191(1), 229-251.
DOI
2021 Burachik, R. S., Caldwell, B. I., & Kaya, C. Y. (2021). A generalized multivariable newton method. Fixed Point Theory and Algorithms for Sciences and Engineering, 2021(15), 1.
DOI
2021 Burachik, R. S., Dao, M. N., & Lindstrom, S. B. (2021). The generalized Bregman distance. SIAM Journal on Optimization, 31(1), 404-424.
DOI
2021 Burachik, R. S., Dao, M. N., & Lindstrom, S. B. (2021). Generalized bregman envelopes and proximity operators. Journal of Optimization Theory and Applications, 190(3), 744-778.
DOI
2020 Burachik, R. S., Canovas, M. J., Roshchina, V., & Sagastizabal, C. (2020). Preface of the special issue error bounds, regularity, and nonsmooth optimization: dedicated to Alexander Kruger on his 65th birthday. Set-Valued and Variational Analysis, 28(1), 1-3.
DOI
2020 Bauschke, H. H., Burachik, R. S., Herman, D. B., & Kaya, C. Y. (2020). On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections. Optimization Letters, 14(8), 1975-1987.
DOI
2020 Burachik, R. S., & Millán, R. D. (2020). A projection algorithm for non-monotone variational inequalities. Set-valued and variational analysis, 28(1), 149-166.
DOI
2020 Arıkan, O., Burachik, R. S., & Kaya, C. Y. (2020). Steklov regularization and trajectory methods for univariate global optimization. Journal of global optimization, 76(1), 91-120.
DOI
2019 Burachik, R., de Pinho, M. D. R., Sagastizabal, C., & Zidani, H. (2019). Preface of the special issue new horizons in optimal control- a special tribute to Helmut Maurer, Urszula Ledzewicz and Heinz Schättler. Set-valued and variational analysis, 27(2), 305-307.
DOI
2019 Burachik, R., Khan, A., Tammer, C., & Ward, D. (2019). Preface - Optimization. Optimization, 68(7), 1261-1263.
DOI
2018 Bauschke, H., Burachik, R., Van Ngai, H., & Phu, H. X. (2018). Preface: Special issue on recent progress in optimization and variational analysis for applications dedicated to Michel Théra's 70th birthday. Vietnam journal of mathematics, 46(1), 1-3.
DOI
2017 Burachik, R. S., & Martínez Legaz, J. E. (2017). On Bregman-type distances for convex functions and maximally monotone operators. Set-valued and variational analysis, 26(2), 369-384.
DOI
2017 Al Homidan, S., Ansari, Q. H., & Burachik, R. S. (2017). Weak sharp solutions for generalized variational inequalities. Positivity, 21(3), 1067-1088.
DOI
2017 Burachik, R. S., & Martín Márquez, V. (2017). An approach for the convex feasibility problem via Monotropic Programming. Journal of mathematical analysis and applications, 453(2), 746-760.
DOI
2017 Burachik, R. S., Yang, X. Q., & Zhou, Y. Y. (2017). Existence of augmented Lagrange multipliers for semi-infinite programming problems. Journal of optimization theory and applications, 173(2), 471-503.
DOI Scopus7 WoS6
2017 Burachik, R. S., Kaya, C. Y., & Rizvi, M. M. (2017). A new scalarization technique and new algorithms to generate pareto fronts. SIAM journal on optimization, 27(2), 1010-1034.
DOI
2016 Burachik, R. S., Kaya, C. Y., & Pinar, M. Ç. (2016). Special issue on "non-linear continuous optimization". EURO journal on computational optimization, 4(1), 1-2.
DOI
2015 Arikan, O., Burachik, R. S., & Kaya, C. Y. (2015). "Backward differential flow" may not converge to a global minimizer of polynomials. Journal of optimization theory and applications, 167(1), 401-408.
DOI
2015 Burachik, R. S., Martinez Legaz, J. E., Rezaie, M., & Théra, M. (2015). An additive subfamily of enlargements of a maximally monotone operator. Set-Valued and Variational Analysis, 23(4), 643-665.
DOI
2015 Burachik, R. S., Iusem, A. N., & Melo, J. G. (2015). The exact penalty map for nonsmooth and nonconvex optimization. Optimization, 64(4), 717-738.
DOI
2014 Burachik, R. S., Kaya, C. Y., & Majeed, S. N. (2014). A duality approach for solving control-constrained linear-quadratic optimal control problems. SIAM journal on control and optimization, 52(3), 1423-1456.
DOI
2014 Burachik, R. S., Kaya, C. Y., & Rizvi, M. M. (2014). A new scalarization technique to approximate Pareto fronts of problems with disconnected feasible sets. Journal of optimization theory and applications, 162(2), 428-446.
DOI
2014 Burachik, R. S., Freire, W., & Kaya, C. Y. (2014). Interior Epigraph Directions method for nonsmooth and nonconvex optimization via generalized augmented Lagrangian duality. Journal of global optimization, 60(3), 501-529.
DOI
2014 Burachik, R. S., & Rizvi, M. M. (2014). Proper efficiency and Proper Karush-Kuhn-Tucker conditions for smooth multiobjective optimization problems. Vietnam Journal of Mathematics, 42(4), 521-531.
DOI
2014 Borwein, J. M., Burachik, R. S., & Yao, L. (2014). Conditions for zero duality gap in convex programming. Journal of nonlinear and convex analysis, 15(1), 167-190.
2014 Burachik, R., Yang, X. Q., & Yang, X. M. (2014). Preface: Special JOTA issue on "Variational Aspects of Vector Optimization". Journal of Optimization Theory and Applications, 162(2), 347-349.
DOI
2013 Burachik, R. S., & Majeed, S. N. (2013). Strong duality for generalized montropic programming in infinite dimensions. Journal of mathematical analysis and applications, 400(2), 541-557.
DOI
2013 Burachik, R. S., Iusem, A. N., & Melo, J. G. (2013). An inexact modified subgradient algorithm for primal-dual problems via augmented Lagrangians. Journal of optimization theory and applications, 157(1), 108-131.
DOI
2012 Burachik, R. S., & Rizvi, M. M. (2012). On weak and strong Kuhn-Tucker conditions for smooth multiobjective optimization. Journal of optimization theory and applications, 155(2), 477-491.
DOI
2012 Avrachenkov, K., Burachik, R. S., Filar, J. A., & Gaitsgory, V. (2012). Constraint augmentation in pseudo-singularly perturbed linear programs. Mathematical programming : series A, 132(1/2), 179-208.
DOI
2012 Burachik, R. S., & Kaya, C. Y. (2012). An augmented penalty function method with penalty parameter updates for nonconvex optimization. Nonlinear analysis, 75(3), 1158-1167.
DOI
2012 Burachik, R. S., Kaya, C. Y., & Sabach, S. (2012). A generalized univariate Newton method motivated by proximal regularization. Journal of optimization theory and applications, 155(3), 923-940.
DOI
2012 Burachik, R., & Kassay, G. (2012). On a generalized proximal point method for solving equilibrium problems in Banach spaces. Nonlinear analysis: theory, methods and applications, 75(18), 6456-6464.
DOI
2011 Burachik, R. S., & Yang, X. (2011). Asymptotic strong duality. Numerical algebra, control and optimization, 1(3), 539-548.
DOI
2011 Burachik, R. S. (2011). On primal convergence for augmented Lagrangian duality. Optimization, 60(8-9), 979-990.
DOI
2010 Burachik, R. S., Kaya, C. Y., & Mammadov, M. (2010). An inexact modified subgradient algorithm for nonconvex optimization. Computational optimization and applications, 45(1), 1-24.
DOI
2010 Burachik, R. S., Iusem, A. N., & Melo, J. G. (2010). Duality and exact penalization for general augmented Lagrangians. Journal of Optimization Theory and Applications, 147(1), 125-140.
DOI WoS22
2010 Burachik, R. S., & Dutta, J. (2010). Inexact proximal point methods for variational inequality problems. SIAM journal on optimization, 20(5), 2653-2678.
DOI
2010 Burachik, R. S., Martinez Legaz, J. E., & Rocco, M. (2010). On a sufficient condition for equality of two maximal monotone operators. Set-valued and variational analysis : theory and applications, 18(3-4), 327-335.
DOI
2010 Burachik, R. S., & Lopes, J. O. (2010). Outer approximation schemes for generalized semi-infinite variational inequality problems. Optimization, 59(4), 601-617.
DOI
2009 Burachik, R. S., Iusem, A., & Melo, J. (2009). A primal dual modified subgradient algorithm with sharp Lagrangian. Journal of global optimization, 46(3), 347-361.
DOI
2009 Burachik, R. S., Lopes, J., & Da, S. G. J. P. (2009). An inexact interior point proximal method for the variational inequality problem. Computational and Applied Mathematics, 28(1), 15-36.
2008 Burachik, R. S., & Rubinov, A. (2008). On abstract convexity and set valued analysis. Journal of nonlinear and convex analysis, 9(1), 105-123.
2008 Burachik, R. S., Drummond, L. M. G., & Scheimberg, S. (2008). On some properties and an application of the logarithmic barrier method. Mathematical programming, 111(1-2), 95-112.
DOI
2007 Burachik, R. S., & Rubinov, A. (2007). Abstract convexity and augmented lagrangians. SIAM journal on optimization, 18(2), 413-436.
DOI Scopus39
2007 Kaya, C. Y., & Burachik, R. S. (2007). An update rule and a convergence result for a penalty function method. Journal of industrial and management optimization.
2006 Burachik, R. S., Sagastizabal, C., & Scheimberg, S. (2006). An inexact method of partial inverses and a parallel bundle method. Optimization methods and software, 21(3), 385-400.
DOI
2006 Burachik, R. S., & Iusem, A. (2006). On non-enlargeable and fully enlargeable monotone operators. Journal of convex analysis.
2006 Burachik, R. S., Gasimov, R., Ismayilova, N., & Kaya, C. Y. (2006). On a modified subgradient algorithm for dual problems via sharp augmented lagrangian. Journal of global optimization, 34(1), 55-78.
DOI
2006 Burachik, R. S., Jeyakumar, V., & Wu, Z. Y. (2006). Necessary and sufficient conditions for stable conjugate duality. Nonlinear analysis, 64(9), 1998-2006.
DOI
2005 Burachik, R. S., & Rubinov, A. (2005). On the absence of duality gap for a family of Lagrange-type functions. Journal of industrial management and optimization, 1(1), 33-38.
DOI
2005 Burachik, R. S., Lopes, J., & Svaiter, B. (2005). An outer approximation method for the variational inequality problem. SIAM journal on control and optimization, 43(6), 2071-2088.
DOI
2005 Burachik, R. S., & Jeyakumar, V. (2005). A dual condition for the convex subdifferential sum formula with applications. Journal of convex analysis.
2005 Burachik, R. S., & Jeyakumar, V. (2005). A new geometric condition for Fenchel's duality in infinite dimensional spaces. Mathematical programming, 104(2-3), 229-233.
DOI
2005 Burachik, R. S., & Fitzpatrick, S. (2005). On a family of convex functions associated to subdifferentials. Journal of nonlinear and convex analysis.
2005 Burachik, R. S., & Jeyakumar, V. (2005). A simple closure condition for the normal cone intersection formula. Proceedings of the American Mathematical Society, 133(6), 1741-1748.
DOI
2003 Burachik, R. S., Scheimberg, S., & Silva, P. (2003). 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.
DOI
2003 Burachik, R. S., & Lopes, J. (2003). A convergence result for an outer approximation scheme. Computational and applied mathematics, 22(3).
DOI
2001 Burachik, R. S., & Scheimberg, S. (2001). A proximal point method for the variational inequality problem in banach spaces. SIAM journal on control and optimization, 39(5), 1633-1649.
DOI

Year Citation
2014 Schulte, R., Burachik, R., & Kaya, Y. (2014). US08644571, Intensity-modulated proton therapy.

  • Optimised networks for synchronisation, load-balance and warfighting dynamics., Defence Science and Technology Group, 22/03/2019 - 30/06/2019

  • Multi-Objective Optimisation for Autonomous UAV Location Planning Over Dynamic Networks, Cwth Dept of Defence, 24/03/2017 - 31/08/2018

Date Role Research Topic Program Degree Type Student Load Student Name
2016 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Miss Stephanie Jane Mills

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