Issue
RAIRO-Oper. Res.
Volume 55, Number 1, January-February 2021
Page(s) 1 - 11
DOI https://doi.org/10.1051/ro/2020066
Published online 03 March 2021
  • A. Ansari Ardali, N. Movahedian and S. Nobakhtian, Convexificators and boundedness of the Kuhn-Tucker multipliers set. Optimization 66 (2017) 1445–1463. [Google Scholar]
  • T. Antczak, Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function. Acta Math. Sci. 37 (2017) 1133–1150. [Google Scholar]
  • A. Ben-Israel and P.D. Robers, A decomposition method for interval linear programming. Manage. Sci. 16 (1970) 374–387. [Google Scholar]
  • F.H. Clarke, Optimization and Nonsmooth Analysis. SIAM 5 (1990). [Google Scholar]
  • G.B. Dantzig, Linear Programming and Extensions. In: Vol. 48 of Princeton Landmarks in Mathematics and Physics. Princeton University Press, Princeton, NJ (1998). [Google Scholar]
  • V.F. Demyanov, Convexification and concavification of a positively homogeneous function by the same family of linear functions. Universia di Pisa, Report 3, 208, 802 (1994). [Google Scholar]
  • V.F. Demyanov and V. Jeyakumar, Hunting for a smaller convex subdifferential. J. Global Optim. 10 (1997) 305–326. [Google Scholar]
  • J. Dutta and S. Chandra, Convexifactors, generalized convexity and optimality conditions. J. Optim. Theory App. 113 (2002) 41–65. [Google Scholar]
  • J. Dutta and S. Chandra, Convexifactors, generalized convexity and vector optimization. Optimization 53 (2004) 77–94. [Google Scholar]
  • G.M. Ewing, Sufficient conditions for global minima of suitably convex functionals from variational and control theory. SIAM Rev. 19 (1977) 202–220. [Google Scholar]
  • J.B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis. Springer, New York, NY (2012). [Google Scholar]
  • J.B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I: Fundamentals. In: Vol. 305 of Series of Comprehensive Studies in Mathematics, Springer, New York, NY (2013). [Google Scholar]
  • H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48 (1990) 219–225. [Google Scholar]
  • V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Opt. Theory App. 101 (1999) 599–621. [Google Scholar]
  • A. Kabgani and M. Soleimani-Damaneh, Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semiinfinite multiobjective optimization using convexificators. Optimization 67 (2017) 217–235. [Google Scholar]
  • A. Kabgani and M. Soleimani-Damaneh, Constraint qualifications and optimality conditions in nonsmooth locally star-shaped optimization using convexificators. Pac. J. Opt. 15 (2019) 399–413. [Google Scholar]
  • N. Kanzi, Necessary optimality conditions for nonsmooth semi-infinite programming problems. J. Global Optim. 49 (2011) 713–725. [Google Scholar]
  • R.N. Kaul and S. Kaur, Generalized convex functions: properties, optimality and duality (No. Systems Optimization Lab. SOL-84-4). Stanford University, Stanford, CA (1984). [Google Scholar]
  • P. Kumar, B. Sharma and J. Dagar, Interval-valued programming problem with infinite constraints. J. Oper. Res. Soc. Chin. 6 (2018) 611–626. [Google Scholar]
  • X.F. Li and J.Z. Zhang, Necessary optimality conditions in terms of convexificators in Lipschitz optimization. J. Optim. Theory App. 131 (2006) 429–452. [Google Scholar]
  • P. Michel and J.P. Penot, A generalized derivative for calm and stable functions. Differ. Integr. Equ. 5 (1992) 433–454. [Google Scholar]
  • B.S. Mordukhovich and Y. Shao, On nonconvex subdifferential calculus in Banach spaces. J. Conv. Anal. 2 (1995) 211–228. [Google Scholar]
  • R. Osuna-Gómez, Y. Chalco-Cano, B. Hernández-Jiménez and G. Ruiz-Garzón, Optimality conditions for generalized differentiable interval-valued functions. Inf. Sci. 321 (2015) 136–146. [Google Scholar]
  • R. Osuna-Gómez, B. Hernádez-Jiménez, Y. Chalco-Cano and G. Ruiz-Gazón, New efficiency conditions for multiobjective interval-valued programming problems. Inf. Sci. 420 (2017) 235–248. [Google Scholar]
  • D. Singh, B.A. Dar and D.S. Kim, KKT optimality conditions in interval-valued multiobjective programming with generalized differentiable functions. Eur. J. Oper. Res. 254 (2016) 29–39. [Google Scholar]
  • L. Stefanini and M. Arana-Jiménez, Karush–Kuhn–Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability. Fuzzy Sets Syst. 362 (2019) 1–34. [Google Scholar]
  • L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal. Theory Methods App. 71 (2009) 1311–1328. [Google Scholar]
  • J.S. Treiman, The linear nonconvex generalized gradient and Lagrange multipliers. SIAM J. Optim. 5 (1995) 670–680. [Google Scholar]
  • L.T. Tung, Karush–Kuhn–Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions. J. Appl. Math. Comput. (2019) 1–25. [Google Scholar]
  • H.C. Wu, The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur. J. Oper. Res. 176 (2007) 46–59. [Google Scholar]
  • H.C. Wu, The Karush–Kuhn–Tucker optimality conditions in multiobjective programming problems with interval-valued objective function. Eur. J. Oper. Res. 196 (2009) 49–60. [Google Scholar]
  • X.Q. Yang, Continuous generalized convex functions and their characterizations. Optimization 54 (2005) 495–506. [Google Scholar]
  • J. Zhang, S. Liu, L. Li and Q. Feng, The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optim. Lett. 8 (2014) 607–631. [Google Scholar]

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