### Dragan Jukić

Josip Juraj Strossmayer University of Osijek

### Research Interests

His research interests were:

- Parameter estimation

- Nonlinear least squares problems

- Curve fitting

- Smoothing methods

- Mathematical modelling

### Biography

Our professor, colleague, and friend, Professor Dragan Jukić, passed away on January 2, 2023, at the age of 61. Professor Jukić played a significant role in establishing the Department of Mathematics at the Josip Juraj Strossmayer University of Osijek, where he also served as the head from 2003 to 2007.

Professor Jukić was born on February 26, 1962, in Bračević near Split. He completed elementary school in Belišće in 1977 and his secondary school in Valpovo in 1981. He graduated at the Faculty of Eduction in Osijek in 1986, earning a degree as a teacher of mathematics and physics. He received his master’s degree in 1990 and his PhD in 1996 from the Department of Mathematics at the Faculty of Science in Zagreb, specializing in applied and numerical mathematics.

He worked as an assistant at the Faculty of Economics in Osijek (1987-1995), and then as a lecturer at the Faculty of Agriculture in Osijek (1995-1997). From 1997, he held the position of assistant professor, and from 2000 as an associate professor at the Faculty of Food Technology in Osijek. From 2002, he was employed as an associate professor at the Department of Mathematics at the University of Osijek. He was appointed to the academic rank of full professor in 2004, and to the permanent position of full professor in 2009.

Professor Jukić’s primary area of scientific interest was applied and numerical mathematics. He published a 39 scientific papers in international journals, 19 papers in conference proceedings, 8 professional papers, and 6 university textbooks.

Since 1996, he was a member of the editorial board of the scientific journal Mathematical Communications, serving as its editor-in-chief from 2014 to 2019. Since its foundation in 2000, he was a member of the editorial board of the professional journal Osječki matematički list.

Since 1996, he was a member of the Program and Organizing Committee of the International Conference on Operational Research organized by the Croatian Operational Research Society. He was also a member of the scientific committee for several international conferences on Applied Mathematics and Scientific Computing. He was a member of the scientific and organizing committee of the Croatian Mathematical Congress.

From 1999 to 2003, he served as the deputy head, from 2007 to 2013 as the assistant head, and from 2003 to 2007 as the head of the Department of Mathematics at the University of Osijek.

### 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

- 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