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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 4
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Articles

Optimality conditions for vector optimization problems with non-cone constraints in image space

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Pages 611-626 | Received 14 Feb 2018, Accepted 24 Jul 2018, Published online: 22 Aug 2018

References

  • Luc DT. Theory of vector optimization. Berlin: Springer; 1989.
  • Jahn J. Vector optimization-theory, applications, extensions. Berlin: Springer; 2004.
  • Tung LT. Strong Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming via Michel-Penot subdifferential. J Nonlinear Funct Anal. 2017;2017: Article ID 49.
  • Tung NL, Luu DV. Optimality conditions for nonsmooth multiobjective optimization problems with general inequality constraints. J Nonlinear Funct Anal. 2018;2018: Article ID 2.
  • Chieu NH, Lee GM, Yen ND. Second-order subdifferentials and optimality conditions for C1-smooth optimization problems. Appl Anal Optim. 2017;1:461–476.
  • Giannessi F, Mastroeni G, Pellegrini L. On the theory of vector optimization and variational inequalities image space analysis and separation. In: Giannessi F, editor. Vector variational inequalities and vector equilibria, mathematical theories. Dordrecht: Kluwer Academic; 2000. p. 153–215. (Nonconvex optimization and its applications; vol. 38).
  • Zhu SK. Image space analysis to Lagrange-type duality for constrained vector optimization problems with applications. J Optim Theory Appl. 2018;177:743–769. doi: 10.1007/s10957-016-1027-6
  • You MX, Li SJ. Separation functions and optimality conditions in vector optimization. J Optim Theory Appl. 2017;175:527–544. doi: 10.1007/s10957-016-1029-4
  • You MX, Li SJ. Nonlinear separation concerning E-optimal solution of constrained multi-objective optimization problems. Optim Lett. 2018;12:123–136. doi: 10.1007/s11590-017-1109-x
  • Flores-Bazán F, Mastroeni G, Vera C. Proper or weak efficiency via saddle point conditions in cone constrained nonconvex vector optimization problems. Departamento de Ingenieria Matematica, Universidad de Concepcion. 2017. Pre-print.
  • Apetrii M, Durea M, Strugariu R. A new penalization tool in scalar and vector optimizations. Nonlinear Anal Theory Methods Appl. 2014;107:22–33. doi: 10.1016/j.na.2014.04.022
  • Durea M, Strugariu R. Vectorial penalization for generalized functional constrained problems. J Glob Optim. 2017;68:899–923. doi: 10.1007/s10898-017-0505-1
  • Castellani G, Giannessi F. Decomposition of mathematical programs by means of theorems of alternative for linear and nonlinear systems. Proceedings of the Ninth International Mathematical Programming Symposium; Survey of Mathematical Programming, Budapest. Amsterdam (North-Holland); 1979. p. 423–439.
  • Giannessi F. Theorems of the alternative and optimality conditions. J Optim Theory Appl. 1984;42:331–365. doi: 10.1007/BF00935321
  • Giannessi F. Constrained optimization and image space analysis, vol. 1: separation of sets and optimality conditions. New York (NY): Springer; 2005.
  • Giannessi F. On the theory of Lagrangian duality. Optim lett. 2007;1:9–20. doi: 10.1007/s11590-006-0013-6
  • Pappalardo M. Image space approach to penalty methods. J Optim Theory Appl. 1990;64:141–152. doi: 10.1007/BF00940028
  • Mastroeni G. Separation methods for vector variational inequalities. Saddle point and gap function. In: Pillo G, Giannessi F, editors. Nonlinear optimization and related topics. Springer; 2000. p. 207–217. (Applied optimization; vol. 36)
  • Mastroeni G. On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation. J Glob Optim. 2012;53:203–214. doi: 10.1007/s10898-011-9674-5
  • Mastroeni G. Nonlinear separation in the image space with applications to penalty methods. Appl Anal. 2012;91:1901–1914. doi: 10.1080/00036811.2011.614603
  • Li J, Feng SQ, Zhang Z. A unified approach for constrained extremum problems: image space analysis. J Optim Theory Appl. 2013;159:69–92. doi: 10.1007/s10957-013-0276-x
  • Li J, Mastroeni G. Image convexity of generalized systems with infinite-dimensional image and applications. J Optim Theory Appl. 2016;169:91–115. doi: 10.1007/s10957-016-0880-7
  • Luo HZ, Mastroeni G, Wu HX. Separation approach for augmented Lagrangians in constrained nonconvex optimization. J Optim Theory Appl. 2010;144:275–290. doi: 10.1007/s10957-009-9598-0
  • Chinaie M, Zafarani J. Nonlinear separation in the image space with applications to constrained optimization. Positivity. 2017;21:1031–1047. doi: 10.1007/s11117-016-0450-0
  • Chen JW, Kobis E, Kobis MA, et al. Optimality conditions for solutions of constrained inverse vector variational inequalities by means of nonlinear scalarization. J Nonlinear Var Anal. 2017;1:145–158.
  • Li GH, Li SJ. Saddle points and gap functions for weak generalized Ky fan inequalities. Optim Lett. 2018;18:1265–1280. doi: 10.1007/s11590-017-1118-9
  • Zhu SK, Li SJ. Unified duality theory for constrained extremum problems. Part I: image space analysis. J Optim Theory Appl. 2014;161:738–762. doi: 10.1007/s10957-013-0468-4
  • Gutiérrez C, Novo V, Ródenas-Pedregosa JL, Tanaka T. Nonconvex separation functional in linear spaces with applications to vector equilibria. SIAM J Optim. 2016;26:2677–2695. doi: 10.1137/16M1063575

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