For a convex programming problem, the Karush–Kuhn–Tucker (KKT) conditions are necessary and sufficient for optimality under suitable constraint qualification. Recently, Suneja et al. [Am. J. Oper. Res. 6 (2013) 536–541] proved KKT optimality conditions for a differentiable vector optimization problem over cones in which they replaced the cone-convexity of constraint function by convexity of feasible set and assumed the objective function to be cone-pseudoconvex. In this paper, we have considered a nonsmooth vector optimization problem over cones and proved KKT type sufficient optimality conditions by replacing convexity of feasible set with the weaker condition considered by Ho [Optim. Lett. 11 (2017) 41–46] and assuming the objective function to be generalized nonsmooth cone-pseudoconvex. Also, a Mond–Weir type dual is formulated and various duality results are established in the modified setting.
Keywords: Vector optimization, cones, generalized nonsmooth cone-pseudoconvex, KKT type optimality conditions, duality
@article{RO_2021__55_S1_S1195_0,
author = {Sharma, Sunila and Yadav, Priyanka},
title = {Optimality and duality in nonsmooth vector optimization with non-convex feasible set},
journal = {RAIRO. Operations Research},
pages = {S1195--S1206},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020050},
mrnumber = {4223142},
zbl = {1511.90383},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020050/}
}
TY - JOUR AU - Sharma, Sunila AU - Yadav, Priyanka TI - Optimality and duality in nonsmooth vector optimization with non-convex feasible set JO - RAIRO. Operations Research PY - 2021 SP - S1195 EP - S1206 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020050/ DO - 10.1051/ro/2020050 LA - en ID - RO_2021__55_S1_S1195_0 ER -
%0 Journal Article %A Sharma, Sunila %A Yadav, Priyanka %T Optimality and duality in nonsmooth vector optimization with non-convex feasible set %J RAIRO. Operations Research %D 2021 %P S1195-S1206 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020050/ %R 10.1051/ro/2020050 %G en %F RO_2021__55_S1_S1195_0
Sharma, Sunila; Yadav, Priyanka. Optimality and duality in nonsmooth vector optimization with non-convex feasible set. RAIRO. Operations Research, Tome 55 (2021), pp. S1195-S1206. doi: 10.1051/ro/2020050
[1] , Optimality and duality in mathematical programming involving generalized convex functions. Ph.D. thesis, University of Delhi, Delhi (1998).
[2] , and , Nonlinear Programming. Wiley, New Jersey (2006). | MR | Zbl
[3] , , and , Pareto Optimality: Game Theory and Equilibria. Springer, New York (2008). | MR | Zbl | DOI
[4] , Optimization and Nonsmooth Analysis. John Wiley & Sons, Inc., New York (1983). | MR | Zbl
[5] , and , Optimality conditions for multiobjective and nonsmooth minimisation in abstract spaces. Bull. Aust. Math. Soc. 50 (1994) 205–218. | MR | Zbl | DOI
[6] , Second-order necessary conditions in locally Lipschitz optimization with inequality constraints. Optim. Lett. 9 (2015) 245–261. | MR | Zbl | DOI
[7] , First-order necessary conditions in locally Lipschitz multiobjective optimization. Optimization 67 (2018) 1447–1460. | MR | Zbl | DOI
[8] , Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems. J. Global Optim. 75 (2019) 111–129. | MR | Zbl | DOI
[9] , Higher-order sufficient conditions for optimization problems with Gâteaux differentiable data. Rev. Roum. Math. Pures Appl. 64 (2019) 25–41. | MR | Zbl
[10] , Nonsmooth multiobjective programming. Numer. Funct. Anal. Optim. 10 (1989) 49–64. | MR | Zbl | DOI
[11] and , Optimality conditions in convex optimization revisited. Optim. Lett. 7 (2013) 221–229. | MR | Zbl | DOI
[12] , Optimality conditions under generalized convexity revisited. Ann. Univ. Buchar. (Math. Ser.) 4(LXII) (2013) 479–490. | MR | Zbl
[13] and , Convex Analysis and Minimization Algorithms I. Springer, Berlin (1993). | Zbl | DOI
[14] , Necessary and sufficient KKT optimality conditions in non-convex optimization. Optim. Lett. 11 (2017) 41–46. | MR | Zbl | DOI
[15] , Higher-order optimality conditions for inequality-constrained problems. Appl. Anal. 92 (2013) 2152–2167. | MR | Zbl | DOI
[16] , On representations of the feasible set in convex optimization. Optim. Lett. 4 (2010) 1–5. | MR | Zbl | DOI
[17] , On multiple-objective optimization with generalized univexity. J. Math. Anal. App. 224 (1998) 131–148. | MR | Zbl | DOI
[18] and , On generalised convex multi-objective nonsmooth programming. J. Aust. Math. Soc. Ser. B 38 (1996) 140–148. | MR | Zbl | DOI
[19] , and , Optimality and duality in nondifferentiable and multiobjective programming under generalized -invexity. J. Global Optim. 29 (2004) 425–438. | MR | Zbl | DOI
[20] , and , Optimality and duality for multiple-objective optimization under generalized type I univexity. J. Math. Anal. App. 303 (2005) 315–326. | MR | Zbl | DOI
[21] , and , Optimality and duality for -invex non-smooth multiobjective programming problems. Optimization 57 (2008) 635–641. | MR | Zbl | DOI
[22] , and , Optimality and duality for a nonsmooth multiobjective optimization involving generalized type I functions. Math. Methods Oper. Res. 67 (2008) 493–504. | MR | Zbl | DOI
[23] and , Generalized concavity and duality. In: Generalized Concavity in Optimization and Economics, edited by and . Academic Press, New York (1981) 263–279. | Zbl
[24] and , Multicriteria optimization methods for design of aircraft control systems, edited by . In: Multicriteria Optimization in Engineering and in the Sciences. Plenum, New York (1981) 225–262. | MR | Zbl
[25] , Multicriteria optimization in mechanics: a survey. Appl. Mech. Rev. 37 (1984) 277–286.
[26] , Multicriteria Optimization in Engineering and in the Sciences. Plenum Press, New York (1988). | MR | Zbl | DOI
[27] , and , Generalized nonsmooth invexity over cones in vector optimization. Eur. J. Oper. Res. 186 (2008) 28–40. | MR | Zbl | DOI
[28] , , and , A different approach to cone-convex optimization. Am. J. Oper. Res. 6 (2013) 536–541.
[29] , and , Optimality and duality for vector optimization problem with non-convex feasible set. OPSEARCH 57 (2020) 1–12. | MR | Zbl | DOI
[30] and , Generalised convexity and duality in multiple objective programming. Bull. Aust. Math. Soc. 39 (1989) 287–299. | MR | Zbl | DOI
Cité par Sources :
