Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems

  • Washington Alves de OliveiraEmail author
  • Marko Antonio Rojas-Medar
  • Antonio Beato-Moreno
  • Maria Beatriz Hernández-Jiménez


If \(x^*\) is a local minimum solution, then there exists a ball of radius \(r>0\) such that \(f(x)\ge f(x^*)\) for all \(x\in B(x^*,r)\). The purpose of the current study is to identify the suitable \(B(x^*,r)\) of the local optimal solution \(x^*\) for a particular multiobjective optimization problem. We provide a way to calculate the largest radius of the ball centered at local Pareto solution in which this solution is optimal. In this process, we present the necessary and sufficient conditions for achieving a global Pareto optimal solution. The results of this investigation might be useful to determine stopping criteria in the algorithms development.


Pareto optimality conditions Multiobjective optimization Quadratic fractional optimization problems 



The authors are indebted to the anonymous reviewers for their helpful comments. This work was supported by the Coordination for the Improvement of Higher Level Personnel of Brazil (CAPES), the Fund to Support Teaching, Research and Extension of Unicamp (FAEPEX) (Grant No. 534/09), the Diretoria Executiva de Relações Internacionais (DERI)—Edital 62—Cátedras Ibero-Americanas (Grant No. 62/17), and the MINECO/ FEDER(UE) (Grant No. MTM2015-66185-P).


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Authors and Affiliations

  1. 1.School of Applied SciencesUniversity of CampinasLimeiraBrazil
  2. 2.Instituto de Alta InvestigaciónUniversidad de TarapacáAricaChile
  3. 3.Department of Statistics and Operations Research, College of MathematicsUniversity of SevillaSevillaSpain
  4. 4.Department of Economics, Quantitative Methods and H. EconomicUniversidad Pablo de OlavideSevillaSpain

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