### Dragan Jukić

School of Applied Mathematics and Informatics

Josip Juraj Strossmayer University of Osijek

Josip Juraj Strossmayer University of Osijek

### Research Interests

- Parameter estimation

- Nonlinear least squares problems

- Curve fitting

- Smoothing methods

- Mathematical modelling

### Degrees

- PhD in mathematics, Department of Mathematics, University of Zagreb, 1996.
- MSc in mathematics, Department of Mathematics, University of Zagreb, 1990.
- BSc in Mathematics and Physics, Josip Juraj Strossmayer University of Osijek, 1986.

### Publications

Journal Publications

- D. Jukić, K. Sabo, An existence criterion for the nonlinear $ell_p-$norm fitting problem, Central European Journal of Operations Research
**29**(2021), 957-966In this paper, we give a necessary and sufficient criterion for the existence of the $ell_p-$norm estimate for the nonlinear $ell_p-$norm fitting problem. Our criterion is based on the existence level that describes the behavior of the objective function as its argument approaches the extended boundary of the parameter space. - D. Jukić, T. Marošević, An existence level for the residual sum of squares of the power-law regression with an unknown location parameter, Mathematica Slovaca
**71**/4 (2021), 1019-1026In a recent paper Jukic [1], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate. - D. Jukić, A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, Journal of Computational and Applied Mathematics,
**375**(2020)In this paper, we provide a necessary and suﬃcient criterion for the existence of the global minima of a continuous lower bounded function deﬁned on a noncompact set. Our criterion is based on a new existence level introduced in this paper that describes the behavior of the function as its argument approaches the extended boundary of the minimization domain. Some examples are included to illustrate the eﬃciency of our criterion. - D. Jukić, An elementary proof of the quadratic envelope characterization of zero-derivative points, Optimization Letters
**12**/5 (2018), 1155-1156This note presents a simple and self-contained proof of Zlobec's theorem [J. Glob. Optim. 46(2010), 155-161] on quadratic envelope characterization of zero-derivative points for smooth functions in several variables with a Lipschitz derivative. Our proof does not require any knowledge about convexifiable functions. - D. Jukić, D. Marković, Nonlinear least squares estimation of the shifted Gompertz distribution, European Journal of Pure and Applied Mathematics
**10**/2 (2017), 157-166The focus of this paper is the existence of the best nonlinear least squares estimate for the shifted Gompertz distribution. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the lp norm (1 ≤ p < ∞ ).

### Projects

- 1-3-2017 – member of scientific project IP-2016-06-6545 “The optimization and statistical models and methods in recognizing properties of data sets measured with errors” (Croatian Science Foundation)
- 2007- 2013 head of scientific program (2352818) “Various aspects of parameter estimation problem in nonlinear mathematical models“ (Ministry of Science, Education and Sports)
- 2007- 2013 head of scientific project (235-2352818-1034) “Nonlinear parameter estimation problems in mathematical models“ (Ministry of Science, Education and Sports)
- 2002- 2005 – scientific project (0235001) “
*Parameter estimation in mathematical models*“ (Department of Mathematics, University of Osijek – Ministry of Science, Education and Sports), investigator - 1996 – 2000 – scientific project (165021) “Parameter identification problems in mathematical models“ (Department of Mathematics, University of Osijek – Ministry of Science and Technology), investigator
- 1991-1995 – scientific project (1-01-129) “Application of numerical and finite mathematics“ (Ministry of Science, Technology and Computing), investigator
- 1986 – 1990 – project task (2.08.01.03.02) “Operationalization of categories and relationships of value laws“ that was carried out within project (2.08.01) “Fundamental research in economy“ (Ministry of Science, Technology and Computing), investigator

### Professional Activities

**Editorial Boards**

- Mathematical Communications, Editor-in-Chief
- Journal of Classical Analysis
- Croatian Operational Research Review
- Osječki matematički list
- 10
^{th}^{ }International Conference on Operational Research (Trogir, Croatia, 2004), Editor

**Committee Memberships**

- Member of the Scientific Committee of the international
*Conference on Applied Mathematics and Scientific Computing*, 2013 (ApplMath13) - Member of the Scientific Committee of the
*5*(Rijeka, 2012)^{th}Croaatian Congress of Mathematics - Member of the Scientific Committee of the international
*Conference on Applied Mathematics and Scientific Computing*, 2011 (ApplMath11) - Member of the Scientific Committee of the international
*Conference on Applied Mathematics and Scientific Computing*, 2009 (ApplMath09) - Member of the Scientific Committee of the 4
^{th}Croaatian Congress of Mathematics (Osijek, 2008) - Member of the Organizing Committee of the
*International**Conference on Operational Research*, Croatian Operational Research Society (1996, 1998, 2000, 2002, 2004) - Member of the Program Committee of the
*International**Conference on Operational Research*, Croatian Operational Research Society (2000, 2002, 2004, 2006, 2008, 2010) - Member of the National Commission for Mathematics, 2005-2021.

**Refereeing/Reviewing**

- Mathematical Communications
- Journal of Classical Analysis
- Osječki matematički list
- AMS Mathematical Review

**Periodically refereeing for journals:**

- Journal of Computational and Applied Mathematics
- Mathematical and Computer Modelling
- European Journal of Operational Research
- Computational Statistics and Data Analysis
- Communications in Statistics – Theory and Methods
- International Journal of Mathematics and Mathematical Sciences
- Information and Software Technology

**Service Activities**

- Assistant Head of the Department of Mathematics, University of Osijek, 2007-2013
- Head of the Department of Mathematics, University of Osijek, 2003 -2007
- Vice-Head of the Department of Mathematics, University of Osijek, 1999-2003
- Head of Engineering Section of the Croatian Mathematical Society-Division Osijek (since 1993)
- Member of the National Commission for Mathematics, 2005-2021

### Personal

- Birthdate: February 26, 1962
- Birthplace: Bračević (near Split), Croatia
- Citizenship: Croatian
- Family: Married, two children