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An existence criterion for the nonlinear \(\ell _p\)-norm fitting problem

Central European Journal of Operations Research volume 29, pages 957–966 (2021)Cite this article

Abstract

In 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.

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References

  • Biggs MC (1971) A new variable metric technique taking account of non-quadratic behaviour of the objective function. IMA J Appl Math 8:315–327

    Article  Google Scholar 

  • Cox G (2020) Almost sure uniqueness of a global minimum without convexity. Ann Stat 48:584–606

    Article  Google Scholar 

  • Demidenko E (1989) Optimization and Regression. Nauka, Moskva (in Russian)

    Google Scholar 

  • Demidenko E (2006) Criteria for global minimum of sum of squares in nonlinear regression. Comput Stat Data Anal 51:1739–1753

    Article  Google Scholar 

  • Demidenko E (2008) Criteria for unconstrained global optimization. J Optim Theory Appl 136:375–395

    Article  Google Scholar 

  • Demidenko E (2017) Exact and approximate statistical inference for nonlinear regression and estimating equation approach. Scand J Stat 44:636–665

    Article  Google Scholar 

  • Gonin R, Money AH (1989) Nonlinear \(L_p\)-norm estimation. Marcel Dekker, New York

    Google Scholar 

  • Hadeler KP, Jukić D, Sabo K (2007) Least squares problems for Michaelis Menten kinetics. Math Methods Appl Sci 30:1231–1241

    Article  Google Scholar 

  • Jukić D (2020) A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. J Comput Appl Math 375:112791

    Article  Google Scholar 

  • Jukić D, Sabo K (2019) An existence criterion for the sum of squares. In: Zadnik Stirn L, Kljajić Borštnar M, Žerovnik J, Drobne S, Povh J (eds) Proceedings of the 15th international symposium on operational research SOR’19, Bled, 25–27 September 2019, pp 500–505

  • Michaelis L, Menten ML (1913) Die Kinetik der Invertinwirkung. Biochem Z 49:333–369

    Google Scholar 

  • Murray JD (1993) Mathematical biology. Springer, Berlin

    Book  Google Scholar 

  • Nakamura T (1984) Existence theorems of a maximum likelihood estimate from a generalized censored data sample. Ann Inst Stat Math 36:375–393

    Article  Google Scholar 

  • Nakamura T, Lee C (1993) On the existence of minimum contrast estimates in binary response model. Ann Inst Stat Math 45:741–758

    Article  Google Scholar 

  • Ross GJS (1990) Nonlinear estimation. Springer, New York

    Book  Google Scholar 

  • Sabo K (2017) Least absolute deviations problem for the Michaelis–Menten function. Math Slovaca 67:245–262

    Article  Google Scholar 

  • Sabo K, Scitovski R, Vazler I (2011) Searching for a best LAD-solution of an overdetermined system of linear equations motivated by searching for a best LAD-hyperplane on the basis of given data. J Optim Theory Appl 149:293–314

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, J.J. Strossmayer University of Osijek, Trg Lj. Gaja 6, 31 000, Osijek, Croatia

    Dragan Jukić & Kristian Sabo

Authors
  1. Dragan Jukić
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  2. Kristian Sabo
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Correspondence to Kristian Sabo.

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This work was supported by the Croatian Science Foundation through Research Grant IP-2016-06-6545.

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Jukić, D., Sabo, K. An existence criterion for the nonlinear \(\ell _p\)-norm fitting problem. Cent Eur J Oper Res 29, 957–966 (2021). https://doi.org/10.1007/s10100-021-00736-7

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  • DOI: https://doi.org/10.1007/s10100-021-00736-7

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