Marko Vrdoljak

Research

Research Interests

Analysis and applied mathematics: calculus of variations and optimal control, homogenization, optimal design

Publications

Papers in scientific journals:

1. P. Kunštek, M. Vrdoljak: A quasi-Newton method in shape optimization for a transmission problem, Optimization Methods & Software (2022), 1-27, http://dx.doi.org/10.1080/10556788.2022.2078823
2. K. Burazin, I. Crnjac, M. Vrdoljak: Optimality criteria method in 2D linearized elasticity problems, Applied Numerical Mathematics 160 (2021), 192-204 http://dx.doi.org/10.1016/j.apnum.2020.10.002
3. P. Kunštek, M. Vrdoljak: Classical optimal designs on annulus and numerical approximations, Journal of Differential Equations 268 (2020) 6920-6939, http://dx.doi.org/10.1016/j.jde.2019.11.077
4. K. Burazin, I. Crnjac, M. Vrdoljak: Variant of optimality criteria method for multiple state optimal design problems, Communications in Mathematical Sciences 16 (2018) 1597-1614 http://dx.doi.org/10.4310/CMS.2018.v16.n6.a5
5. M. Vrdoljak: Multiple state optimal design problems with random perturbation, Electronic Journal of Differential Equations 2018 (2018), No. 59, pp. 1-10
6. K. Burazin, M. Vrdoljak: Exact Solutions in Optimal Design Problems for Stationary Diffusion Equation, Acta Applicandae Mathematicae (2018) 1-18.
7. K. Burazin, J. Jankov, M. Vrdoljak: Homogenization of elastic plate equation, Mathematical Modelling and Analysis 23 (2018) 190-204
8. M. Vrdoljak: Classical Optimal Design in Two-Phase Conductivity Problems, SIAM Journal on Control and Optimization 54 (2016) 2020-2035
9. K. Burazin, M. Vrdoljak: Homogenisation theory for Friedrichs systems, Communications on Pure and Applied Analysis 13 (2014) 1017-1044
10. N. Antonić, K. Burazin, M. Vrdoljak: Second-order equations as Friedrichs systems, Nonlinear Analysis B: Real World Applications 14 (2014) 290-305
11. N. Antonić, K. Burazin, M. Vrdoljak: Heat equation as a Friedrichs system, Journal of Mathematical Analysis and Applications 404 (2013) 537-553
12. N. Antonić, K. Burazin, M. Vrdoljak: Connecting classical and abstract theory of Friedrichs systems via trace operator, ISRN Mathematical Analysis (2011), Art. ID 469795, 14 p.
13. N. Antonić, M.Vrdoljak: Partial relaxation and optimal design problems, International mathematical forum 33 (2011) 1601-1611
14. M. Vrdoljak: Optimality criteria method for optimal design in hyperbolic problems, Mathematical Communications 15 (2010) 555-572
15. M. Vrdoljak: On Hashin-Shtrikman bounds for mixtures of two isotropic materials, Nonlinear Analysis B: Real World Applications 11 (2010) 4597-4606
16. N. Antonić, M. Vrdoljak: Parabolic H-convergence and small-amplitude homogenization, Applicable Analysis 88 (2009) 1493-1508
17. N. Antonić, M.Vrdoljak: Small-Amplitude homogenisation of diffusion equation, International Journal of Pure and Applied Mathematics 50 (2009) 233-238
18. M. Vrdoljak: Multiple state optimal design problems and Hashin-Shtrikman bounds, International Journal of Pure and Applied Mathematics 42 (2008) 319--324
19. N. Antonić, M. Vrdoljak: Gradient methods for multiple state optimal design problems, Annali dell'Universita di Ferrara 53 (2007) 177-187
20. N. Antonić, M. Vrdoljak: Sequential laminates in multiple-state optimal design problems, Mathematical Problems in Engineering (2006) Art. ID 68695, 14 p.
21. N. Antonić, M. Vrdoljak: On some projections of homogenised coefficients for stationary diffusion equation, Proc. Appl. Math. Mech. 3 (2003) 440-441
22. N. Antonić, N. Balenović, M. Vrdoljak: Optimal design for vibrating plates, Zeitschrift fur Angewandte Mathematik und Mechanik 80 suppl. 3 (2000) 783-784
23. N. Antonić, M. Vrdoljak: Optimal design and hyperbolic problems, Mathematical Communications 4 (1999) 121-129

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Short CV