Approximate optimality conditions for approximate efficiency in semi-infinite multiobjective fractional programming problem

Moustaid, Mohamed Bilal; Dali, Issam

doi:10.2478/candc-2024-0019

Abstract

In this paper, we obtain approximate necessary and sufficient optimality conditions, characterizing an approximately efficient solution of a semi-infinite multiobjective fractional problem under the closedness qualification condition. As a consequence, we derive approximate necessary and sufficient optimality conditions characterizing an approximately efficient solution for a constrained multiobjective fractional programming problem. Furthermore, we present examples illustrating our main results.

References

Bot, R. I. (2009) Conjugate Duality in Convex Optimization. 637. Springer Science & Business Media.
Search in Google Scholar Back to article
Bot, R. I., Grad, S.-M. and Wanka, G. (2009) Duality in Vector Optimization. Springer Science & Business Media.
Search in Google Scholar Back to article
Burachik, R. and Jeyakumar, V. (2005) A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal., 15: 540–554.
Search in Google Scholar Back to article
Chuong, T. D. (2016) Nondifferentiable fractional semi-infinite multiobjective optimization problems. Operations Research Letters, 44(2): 260–266.
Search in Google Scholar Back to article
Chuong, T. D. and Kim, D. S. (2014) Nonsmooth semi-infinite multiobjective optimization problems. J. Optim. Theory Appl., 160(3): 748–762.
Search in Google Scholar Back to article
Deng, S. (1997) On approximate solutions in convex vector optimization. SIAM Journal on Control and Optimization, 35(6): 2128–2136.
Search in Google Scholar Back to article
Dutta, J. and Vetrivel, V. (2001) On approximate minima in vector optimization. Numer. Funct. Anal. Optim., 22(7-8): 845–859.
Search in Google Scholar Back to article
Goberna, M. A. and López Cerda, M. A. (1998) Linear Semi-Infinite Optimization. Wiley. Chichester.
Search in Google Scholar Back to article
Guo, F. and Jiao, L. (2021) On solving a class of fractional semi-infinite polynomial programming problems. Comput. Optim. Appl., 80(2): 439–481.
Search in Google Scholar Back to article
Gutiérrez, C., Jiménez, B. and Novo, V. (2005) Multiplier rules and saddlepoint theorems for Helbig’s approximate solutions in convex Pareto problems. J. Glob. Optim., 32(3): 367–383.
Search in Google Scholar Back to article
Gutiérrez, C., Jiménez, B., and Novo, V. (2006) ǫ-Pareto optimality conditions for convex multiobjective programming via Max function. Numer. Funct. Anal. Optim., 27(1): 57–70.
Search in Google Scholar Back to article
Jeyakumar, V. (2003) Characterizing set containments involving infinite convex constraints and reverse-convex constraints. SIAM J. Optim., 13(4): 947–959.
Search in Google Scholar Back to article
Jeyakumar, V., Lee, G. M. and Dinh, N. (2003) New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. SIAM J. Optim., 14(2): 534–547.
Search in Google Scholar Back to article
Jeyakumar, V., Rubinov, A. M., Glover, B. M. and Ishizuka, Y. (1996) Inequality systems and global optimization. J. Math. Anal. Appl., 202(3): 900–919.
Search in Google Scholar Back to article
Jiao, L., Lee, J. H. and Zhou, Y. (2020) A hybrid approach for finding efficient solutions in vector optimization with sos-convex polynomials. Oper. Res. Lett., 48: 188–194.
Search in Google Scholar Back to article
Kerdkaew, J. and Wangkeeree, R. (2020) Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty. J. Ind. Manag. Optim., 16: 2651–2673.
Search in Google Scholar Back to article
Kim, M. H., Kim, G. S. and Lee, G. M. (2011) On ǫ-optimality conditions for multiobjective fractional optimization problems. Fixed Point Theory Appl., 2011: 13.
Search in Google Scholar Back to article
Kuroiwa, D. and Lee, G. M. (2012) On robust multiobjective optimization. Vietnam J. Math., 40: 305–317.
Search in Google Scholar Back to article
Kutateladze, S. S. (1979) Convex ɛ-programming. Sov. Math., Dokl., 20: 391–393.
Search in Google Scholar Back to article
Lee, J. H. and Lee, G. M. (2018) On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems. Ann. Oper. Res., 269(1-2): 419–438.
Search in Google Scholar Back to article
Li, X.-B., Wang, Q.-L. and Lin, Z. (2019) Optimality conditions and duality for minimax fractional programming problems with data uncertainty. J. Ind. Manag. Optim., 15(3): 1133–1151.
Search in Google Scholar Back to article
Liu, J., Long, X.-J. and Huang, N.-J. (2023) Approximate optimality conditions and mixed type duality for semi-infinite multiobjective programming problems involving tangential subdifferentials. J. Ind. Manag. Optim., 19(9): 6500–6519.
Search in Google Scholar Back to article
Liu, J. C. (1992) ɛ-duality theorem of nondifferentiable nonconvex multiobjective programming. J. Optim. Theory Appl., 74(3): 567–568.
Search in Google Scholar Back to article
Liu, J. C. (1996) ɛ-Pareto optimality for nondifferentiable multiobjective programming via penalty function. J. Math. Anal. Appl., 198(1): 248— -61.
Search in Google Scholar Back to article
Liu, J.-C. and Yokoyama, K. (1999) ɛ-optimality and duality for multiobjective fractional programming. Comput. Math. Appl., 37(8): 119–128.
Search in Google Scholar Back to article
Loridan, P. (1984) ɛ-solutions in vector minimization problems. J. Optim. Theory Appl., 43: 265–276.
Search in Google Scholar Back to article
Moustaid, M., Laghdir, M. and Dali, I. (2022a) Sequential optimality conditions of approximate proper efficiency for a multiobjective fractional programming problem. SeMA Journal, 80(4), 611–627.
Search in Google Scholar Back to article
Moustaid, M. B., Rikouane, A. Dali, I. and Laghdir, M. (2022b) Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brondsted-Rockafellar approximate subdifferential. Rend. Circ. Mat. Palermo (2), 71(2): 737–754.
Search in Google Scholar Back to article
Pham, T.-H. (2023) On isolated/properly efficient solutions in nonsmooth robust semi-infinite multiobjective optimization. Bull. Malays. Math. Sci. Soc. (2), 46(2): 31.
Search in Google Scholar Back to article
Singh, V., Jayswal, A., Stancu-Minasian, I. and Rusu-Stancu, A. M. (2021) Isolated and proper efficiencies for semi-infinite multiobjective fractional problems. Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., 83(3): 111–124.
Search in Google Scholar Back to article
Sun, X., Feng, X. and Teo, K. L. (2022) Robust optimality, duality and saddle points for multiobjective fractional semi-infinite optimization with uncertain data. Optim. Lett., 16(5): 1457–1476.
Search in Google Scholar Back to article
Sun, X., Huang, J. and Teo, K. L. (2024) On semidefinite programming relaxations for a class of robust sos-convex polynomial optimization problems. J. Glob. Optim., 88: 755–776.
Search in Google Scholar Back to article
Sun, X., Tan, W. and Teo, K. L. (2023) Characterizing a class of robust vector polynomial optimization via sum of squares conditions. J. Optim. Theory Appl., 197: 737–764.
Search in Google Scholar Back to article
Sun, X., Teo, K. L. and Long, X.-J. (2021) Some characterizations of approximate solutions for robust semi-infinite optimization problems. J. Glob. Optim., 191: 281–310.
Search in Google Scholar Back to article
White, D. J. (1986) Epsilon efficiency. J. Optim. Theory Appl., 49: 319–337.
Search in Google Scholar Back to article
Zeng, J., Xu, P. and Fu, H. (2019) On robust approximate optimal solutions for fractional semi-infinite optimization with uncertainty data. J. Inequal. Appl., 2019: 16.
Search in Google Scholar Back to article

Approximate optimality conditions for approximate efficiency in semi-infinite multiobjective fractional programming problem

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