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Articles

Pascoletti-Serafini scalarization and vector optimization with a variable ordering structure

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Pages 917-931 | Received 01 May 2017, Published online: 24 Sep 2018

References

  • M. Alshahrani, Q. H. Ansari, S. Al-Homidan, Nonsmooth variational-like inequalities and nonsmooth vector optimization, Optimization Letters. 8(2) (2014), 739–751. doi: 10.1007/s11590-013-0614-9
  • T.Q. Bao and B.S. Mordukhovich, Necessary nondomination conditions in set and vector optimization with variable ordering structures, J. Optim. Theory Appl. 162 (2014), 350–370. doi: 10.1007/s10957-013-0332-6
  • T.Q. Bao, B.S. Mordukhovich and A. Soubeyran, Variational analysis in psychological modeling, J. Optim. Theory Appl. 164 (2015), 290–315. doi: 10.1007/s10957-014-0569-8
  • K. Bergstresser, A. Charnes and P.L. Yu, Generalization of domination structures and nondominated solutions in multicriteria decision making, J. Optim. Theory Appl. 18 (1976), 3–13. doi: 10.1007/BF00933790
  • J.Y. Bello Cruz and G. Bouza Allende, A steepest descent-like method for variable order vector optimization problems, J. Optim. Theory Appl. 162 (2014), 371–391. doi: 10.1007/s10957-013-0308-6
  • G.Y. Chen, Existence of solutions for a vector variational inequality: an extension of the Hartmann-Stampacchia Theorem, J. Optim. Theory Appl. 74 (1992), 445–456. doi: 10.1007/BF00940320
  • G.Y. Chen, X. Huang and X.Q. Yang, Vector Optimization, Set-Valued and Variational Analysis, Springer, Berlin, (2005).
  • A. Cambini, A. Marchi and L. Martein, On nonlinear scalarization in vector optimization, J. Info. Optim. Sci. 17(2) (1996), 373–385.
  • G.Y. Chen and X.Q. Yang, Characterizations of variable domination structures via nonlinear scalarizationn, J. Optim. Theory Appl. 112 (2002), 97–110. doi: 10.1023/A:1013044529035
  • G.Y. Chen, X.Q. Yang and H. Yu, A nonlinear scalarization function and generalized quasi-vector equilibrium problems, J. Global Optim. 32 (2005), 451–466. doi: 10.1007/s10898-003-2683-2
  • S. Dafermos, Exchange price equilibrium and variational inequalities, Math. Program. 46 (1990), 391–402. doi: 10.1007/BF01585753
  • M. Durea, R. Strugariu and C. Tammer, On set-valued optimization problems with variable ordering structure, J. Global Optim. 61 (2015), 745–767. doi: 10.1007/s10898-014-0207-x
  • G. Eichfelder, Adaptive Scalarization Methods in Multiobjective Optimization, Springer, Berlin, (2008).
  • G. Eichfelder, Optimal elements in vector optimization with a variable ordering structure, J. Optim. Theory Appl. 151 (2011), 217–240. doi: 10.1007/s10957-011-9928-x
  • G. Eichfelder, Variable Ordering Structures in Vector Optimization, Springer, Berlin, (2014).
  • G. Eichfelder, Numerical procedures in multiobjective optimization with a variable ordering structures, J. Optim. Theory Appl. 162 (2014), 489–514. doi: 10.1007/s10957-013-0267-y
  • G. Eichfelder and R. Kasimbeyli, Properly optimal elements in vector optimization with variable ordering structures, J. Global Optim. 60 (2014), 689–712. doi: 10.1007/s10898-013-0132-4
  • A. Engau, Variable preference modeling with ideal-symmetric convex cones, J. Global Optim. 42 (2008), 295–311. doi: 10.1007/s10898-007-9246-x
  • A. Hamel, Translative sets and functions and their applications to risk measure theory and nonlinear separation, Preprint series of IMPA, Rio de Janeiro, 21 (2006).
  • P.T. Harker, J.S. Pang, Finite dimensional variational inequality and nonlinear complementarity problems: a survey of theory, Math. Program., 48 (1990), 161–220. doi: 10.1007/BF01582255
  • N.T.T. Huong and N.D. Yen, The Pascoletti-Serafini scalarization scheme and linear vector optimization, J. Optim. Theory Appl. 162 (2014), 559–576. doi: 10.1007/s10957-013-0294-8
  • J. Jahn, Vector Optimization, Theory, Application, and Extentions, Springer, Berlin, (2004).
  • A. Pascoletti and P. Serafini, Scalarization vector optimization problems, J. Optim. Theory Appl. 42 (1984), 499–524. doi: 10.1007/BF00934564
  • M. Rocca, Well-posed vector optimization problems and vector variational inequalities, J. Information & Optimization Sciences 27(2) (2006), 259–270. doi: 10.1080/02522667.2006.10699691
  • B. Soleimani, Characterization of approximate solutions of vector optimization problems with a variable order structure, J. Optim. Theory Appl. 162 (2014), 605–632. doi: 10.1007/s10957-014-0535-5
  • B. Soleimani and C. Tammer, Concepts for approximate solutions of vector optimization problems with variable order structures,  Vietnam J. Math. 42 (2014), 543–566. doi: 10.1007/s10013-014-0103-1
  • Y.D. Xu and S.J. Li, A new nonlinear scalarization function and applications, Optimization. 65 (2016), 207–231. 207–231. doi: 10.1080/02331934.2015.1014479
  • P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), 319–377. doi: 10.1007/BF00932614

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