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Publications

Habilitation Thesis

    E. R. Csetnek (2016) - Recent advances in splitting methods for monotone inclusions and nonsmooth optimization problems, University of Vienna (PDF)

PhD Thesis

    E. R. Csetnek (2009) - Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization. Applications of the duality theory to enlargements of maximal monotone operators, Logos Verlag Berlin, 2010, ISBN 978-3-8325-2503-3

Papers

    Preprints

  1. E.R. Csetnek and M.A. Karapetyants - A fast continuous time approach for non-smooth convex optimization with time scaling and Tikhonov regularization, arXiv:2207.12023
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    To appear

  2. R.I. Boţ, E.R. Csetnek and D.-K. Nguyen - Fast OGDA in continuous and discrete time, to appear in Foundations of Computational Mathematics arXiv:2203.10947
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    Journal publications

  3. R. I. Boţ, E. R. Csetnek, S.C. László (2024) - On the strong convergence of continuous Newton-like inertial dynamics with Tikhonov regularization for monotone inclusions, Journal of Mathematical Analysis and Applications 530(2), Article 127689
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  4. R.I. Boţ, E.R. Csetnek and M. Sedlmayer (2023) - An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function, Computational Optimization and Applications 86(3), 925-966
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  5. H. Attouch, R.I. Boţ and E.R. Csetnek (2023) - Fast optimization via inertial dynamics with closed-loop damping, Journal of the European Mathematical Society 25(5), 1985-2056
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  6. R.I. Boţ, E.R. Csetnek and D.-K. Nguyen (2023) - Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates, Mathematical Programming 200(1), 147-197
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  7. A. Böhm, M. Sedlmayer, E.R. Csetnek and R.I. Boţ (2022) - Two steps at a time -- taking GAN training in stride with Tseng's method, SIAM Journal on Mathematics of Data Science 4(2), 750-771
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  8. E. R. Csetnek, A. Eberhard, M.K. Tam (2021) - Convergence Rates for Boundedly Regular Systems, Advances in Computational Mathematics 47:62
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  9. R. I. Boţ, E. R. Csetnek, S. László (2021) - Tikhonov regularization of a second order dynamical system with Hessian driven damping, Mathematical Programming 189(1), 151-186
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  10. S. Bitterlich, E. R. Csetnek, G. Wanka (2021) - A Dynamical Approach to Two-Block Separable Convex Optimization Problems with Linear Constraints, Numerical Functional Analysis and Optimization 42(1), 1-38
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  11. S. Banert, R. I. Boţ, E. R. Csetnek (2021) - Fixing and extending some recent results on the ADMM algorithm, Numerical Algorithms 86(3), 1303-1325
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  12. E. R. Csetnek (2020) - Continuous dynamics related to monotone inclusions and non-smooth optimization problems, Set Valued and Variational Analysis 28(4), 611-642
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  13. R. I. Boţ, E. R. Csetnek, S. László (2020) - A primal-dual dynamical approach to structured convex minimization problems, Journal of Differential Equations 269(5), 10717-10757
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  14. R. I. Boţ, E. R. Csetnek, P.T. Vuong (2020) - The forward-backward-forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces, EJOR (European Journal of Operational Research) 287, 49-60
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  15. R. I. Boţ, E. R. Csetnek, S. László (2020) - A second order dynamical approach with variable damping to nonconvex smooth minimization, Applicable Analysis 99(3), 361-378
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  16. E. R. Csetnek, Y. Malitsky and M.K. Tam (2019) - Shadow Douglas-Rachford Splitting for Monotone Inclusions, Applied Mathematics and Optimization 80(3), 665-678
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  17. R. I. Boţ, E. R. Csetnek, D. Meier (2019) - Variable metric ADMM for solving variational inequalities with monotone operators over affine sets, in: H.H. Bauschke, R.S. Burachik, R. D. Luke (Eds.), "Splitting Algorithms, Modern Operator Theory, and Applications", Springer Nature, Heidelberg, 91-112
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  18. R. I. Boţ, E. R. Csetnek (2019) - A second order dynamical system with Hessian-driven damping and penalty term associated to variational inequalities, Optimization, 68(1), 1855-1880
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  19. S. Bitterlich, R. I. Boţ, E. R. Csetnek, G. Wanka (2019) - The Proximal Alternating Minimization Algorithm for two-block separable convex optimization problems with linear constraints, Journal of Optimization Theory and Applications 182(1), 110–132
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  20. R. I. Boţ, E. R. Csetnek, Dang-Khoa Nguyen (2019) - A proximal minimization algorithm for structured nonconvex and nonsmooth problems, SIAM Journal on Optimization 29(2), 1300–1328
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  21. R. I. Boţ, E. R. Csetnek, D. Meier (2019) - Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces, Optimization Methods and Software 34(3), 489-514
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  22. R. I. Boţ, E. R. Csetnek (2019) - Newton-like dynamics associated to nonconvex optimization problems, in: S. Hosseini, B.S. Mordukhovich, A. Uschmajew (Eds.), "Nonsmooth Optimization and Its Applications", International Series of Numerical Mathematics, Vol. 170, Springer Nature, Cham, 131-149 arXiv:1703.01339
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  23. R. I. Boţ, E. R. Csetnek (2019) - ADMM for monotone operators: convergence analysis and rates, Advances in Computational Mathematics 45(1), 327-359
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  24. R. I. Boţ, E. R. Csetnek, S. László (2018) - Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems, Journal of Evolution Equations 18(3), 1291-1318
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  25. R. I. Boţ, E. R. Csetnek, S. László (2018) - Second order dynamical systems with penalty terms associated to monotone inclusions, Analysis and Applications 6(5), 601-622
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  26. R. I. Boţ, E. R. Csetnek (2018) - Approaching nonsmooth nonconvex optimization problems through first order dynamical systems with hidden acceleration and Hessian driven damping terms, Set-Valued and Variational Analysis 26(2), 227-245
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  27. R. I. Boţ, E. R. Csetnek (2018) - A forward-backward dynamical approach to the minimization of the sum of a nonsmooth convex with a smooth nonconvex function, ESAIM: Control, Optimisation and Calculus of Variations 24(2), 463-477
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  28. R. I. Boţ, E. R. Csetnek, N. Nimana (2018) - An inertial proximal-gradient penalization scheme for constrained convex optimization problems, Vietnam Journal of Mathematics 46, 53-71
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  29. R. I. Boţ, E. R. Csetnek, N. Nimana (2018) - Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data, Optimization Letters 12, 17–33
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  30. R. I. Boţ, E. R. Csetnek (2018) - Convergence rates for forward-backward dynamical systems associated with strongly monotone inclusions, Journal of Mathematical Analysis and Applications 457(2), 1135-1152
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  31. R. I. Boţ, E. R. Csetnek (2017) - Levenberg-Marquardt dynamics associated to variational inequalities, Set-Valued and Variational Analysis 25, 569-589
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  32. R. I. Boţ, E. R. Csetnek (2017) - Proximal-gradient algorithms for fractional programming, Optimization 66(8), 1383-1396
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  33. R. I. Boţ, E. R. Csetnek (2017) - Penalty schemes with inertial effects for monotone inclusion problems, Optimization 66(6), 965-982
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  34. R. I. Boţ, E. R. Csetnek (2017) - A dynamical system associated with the fixed points set of a nonexpansive operator, Journal of Dynamics and Differential Equations 29(1), 155-168
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  35. R. I. Boţ, E. R. Csetnek (2017) - Second order dynamical systems associated to variational inequalities, Applicable Analysis 96(5), 799-809
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  36. R. I. Boţ, E. R. Csetnek (2016) - Approaching monotone inclusion problems via second order dynamical systems with linear and anisotropic damping, in: V. Barbu, C. Lefter, I.I. Vrabie (Eds.), "New Trends in Differential Equations, Control Theory and Optimization", Proceedings of the 8th Congress of Romanian Mathematicians, World Scientific Publishing, Singapore, 53-72 (PDF)
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  37. R. I. Boţ, E. R. Csetnek (2016) - An inertial Tseng's type proximal algorithm for nonsmooth and nonconvex optimization problems, Journal of Optimization Theory and Applications 171(2), 600-616
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  38. R. I. Boţ, E. R. Csetnek (2016) - Second order forward-backward dynamical systems for monotone inclusion problems, Siam Journal on Control and Optimization 54(3), 1423-1443
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  39. R. I. Boţ, E. R. Csetnek, S. László (2016) - An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions, EURO Journal on Computational Optimization 4, 3-25
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  40. R. I. Boţ, E. R. Csetnek (2016) - An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems, Numerical Algorithms 71, 519-540
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  41. R. I. Boţ, E. R. Csetnek (2016) - An inertial alternating direction method of multipliers, Minimax Theory and its Applications 1(1), 29-49
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  42. R. I. Boţ, E. R. Csetnek (2016) - Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems, Journal of Mathematical Analysis and Applications 435(2), 1688-1700
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  43. R. I. Boţ, E. R. Csetnek (2015) - A hybrid proximal-extragradient algorithm with inertial effects, Numerical Functional Analysis and Optimization 36(8), 951-963
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  44. R. I. Boţ, E. R. Csetnek, A. Heinrich, C. Hendrich (2015) - On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems, Mathematical Programming 150(2), 251-279
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  45. R. I. Boţ, E. R. Csetnek, C. Hendrich (2015) - Inertial Douglas-Rachford splitting for monotone inclusion problems, Applied Mathematics and Computation 256, 472-487
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  46. R. I. Boţ, E. R. Csetnek (2015)- On the convergence rate of a forward-backward type primal-dual splitting algorithm for convex optimization problems, Optimization 64(1), 5-23
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  47. R. I. Boţ, E. R. Csetnek (2014) - A Tseng's type penalty scheme for solving inclusion problems involving linearly composed and parallel-sum type monotone operators, Vietnam Journal of Mathematics 42(4), 451-465
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  48. R. I. Boţ, E. R. Csetnek, C. Hendrich (2014) - Recent developments on primal-dual splitting methods with applications to convex minimization, in: P.M. Pardalos, T.M. Rassias (Eds.), "Mathematics Without Boundaries: Surveys in Interdisciplinary Research", Springer-Verlag, New York (PDF)
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  49. R. I. Boţ, E. R. Csetnek (2014) - Forward-Backward and Tseng's Type Penalty Schemes for Monotone Inclusion Problems, Set-Valued and Variational Analysis 22, 313-331
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  50. R. I. Boţ, E. R. Csetnek, E. Nagy (2013) - Solving systems of monotone inclusions via primal-dual splitting techniques, Taiwanese Journal of Mathematics 17(6), 1983-2009
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  51. R. I. Boţ, E. R. Csetnek (2013) - Conjugate duality and the control of linear discrete systems, Journal of Optimization Theory and Applications 159(3), 576-589
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  52. R. I. Boţ, E. R. Csetnek, A. Heinrich (2013) - A primal-dual splitting algorithm for finding zeros of sums of maximal monotone operators, SIAM Journal on Optimization 23(4), 2011-2036
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  53. R. I. Boţ, E. R. Csetnek (2013) - A Brøndsted-Rockafellar theorem for diagonal subdifferential operators, in: D. Bailey, H.H. Bauschke, P. Borwein, F. Garvan, M. Théra, J. Vanderwerff, H. Wolkowicz (Eds.), "Computational and Analytical Mathematics", Springer-Verlag, New York, 99-106 (PDF)
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  54. L. Cioban, E.R. Csetnek (2013) - Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality, Central European Journal of Mathematics, 11(5), 829-850
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  55. L. Cioban, E. R. Csetnek (2012) - Duality for ε-variational inequalities via the subdifferential calculus, Nonlinear Analysis: Theory, Methods & Applications, 75(6), 3142-3156
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  56. R. I. Boţ, E. R. Csetnek (2012) - Error bound results for convex inequality systems via conjugate duality, TOP 20(2), 296-309
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  57. R. I. Boţ, E. R. Csetnek (2012) - On some erroneous statements in the paper "Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications" by A. Capătă, Journal of Optimization Theory and Applications 153(2), 546-550
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  58. R. I. Boţ, E. R. Csetnek (2012) - Regularity conditions via generalized interiority notions in convex optimization: new achievements and their relation to some classical statements, Optimization 61(1), 35-65
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  59. R. I. Boţ, E. R. Csetnek (2011) - A comparison of some recent regularity conditions for Fenchel duality, in: H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, H. Wolkowicz (Eds.), "Fixed-Point Algorithms for Inverse Problems in Science and Engineering", Springer Optimization and Its Applications, Springer-Verlag, New York, 111-130 (PDF)
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  60. R. I. Boţ, E. R. Csetnek (2010) - On a zero duality gap result in extended monotropic programming, Journal of Optimization Theory and Applications 147(3), 473-482
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  61. R. I. Boţ, E. R. Csetnek (2010) - On extension results for n-cyclically monotone operators in reflexive Banach spaces, Journal of Mathematical Analysis and Applications 367(2), 693-698
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  62. R. I. Boţ, E. R. Csetnek (2009) - On Two properties of enlargements of maximal monotone operators, Journal of Convex Analysis 16(3-4), 713-725
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  63. R. I. Boţ, E. R. Csetnek (2009) - Enlargements of positive sets, Journal of Mathematical Analysis and Applications 356(1), 328-337
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  64. R. I. Boţ, E. R. Csetnek (2009) - On an open problem regarding totally Fenchel unstable functions, Proceedings of the American Mathematical Society 137(5), 1801-1805
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  65. R. I. Boţ, E. R. Csetnek, G. Wanka (2008) - On some abstract convexity notions in real linear spaces, Mathematical Inequalities & Applications 11(3), 571-583
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  66. R. I. Boţ, E. R. Csetnek (2008) - An application of the bivariate inf-convolution formula to enlargements of monotone operators, Set-Valued Analysis 16(7-8), 983-997
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  67. R. I. Boţ, E. R. Csetnek, A. Moldovan (2008) - Revisiting some duality theorems via the quasirelative interior in convex optimization, Journal of Optimization Theory and Applications 139(1), 67-84
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  68. R. I. Boţ, E. R. Csetnek, G. Wanka (2008) - Regularity conditions via quasi-relative interior in convex programming, SIAM Journal on Optimization 19(1), 217-233
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  69. R. I. Boţ, E. R. Csetnek, G. Wanka (2008) - Sequential optimality conditions for composed convex optimization problems, Journal of Mathematical Analysis and Applications 342(2), 1015-1025
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  70. R. I. Boţ, E. R. Csetnek, G. Wanka (2008)- Sequential optimality conditions in convex programming via perturbation approach, Journal of Convex Analysis 15(1), 149-164
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  71. R. I. Boţ, E. R. Csetnek, G. Wanka (2007) - A new condition for maximal monotonicity via representative functions, Nonlinear Analysis: Theory, Methods & Applications 67(8), 2390-2402

Other Works

  • E. R. Csetnek (2005) - Hyperconvex metric spaces, Master thesis, ''Babeş-Bolyai''-University Cluj-Napoca
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  • E. R. Csetnek (2004) - Kurzweil integrals, Diploma thesis, ''Babeş-Bolyai''-University Cluj-Napoca
Ernö Robert Csetnek
Faculty of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Vienna
Austria
T: +43-1-4277-50768
robert.csetnek@univie.ac.at
University of Vienna | Universitätsring 1 | 1090 Vienna | T +43-1-4277-0
E. R. Csetnek (2009) - Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization. Applications of the duality theory to enlargements of maximal monotone operators, Chemnitz University of Technology (PDF)