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

• Autorzy: Moustaid Mohamed Bilal , Dali Issam

Identyfikatory

DOI

10.2478/candc-2024-0019

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fractional semi-infinite multiobjective optimization; multiobjective fractional programming problem; max-function aproach; approximate efficient solution; approximate optimality conditions

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2024
• Tom: Vol. 53, No. 3
• Strony: 429--455
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Moustaid Mohamed Bilal

• Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco

autor

Dali Issam

• Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco

Bibliografia

• Bot, R. I. (2009) Conjugate Duality in Convex Optimization. 637. Springer Science & Business Media.
• Bot, R. I., Grad, S.-M. and Wanka, G. (2009) Duality in Vector Optimization. Springer Science & Business Media.
• Burachik, R. and Jeyakumar, V. (2005) A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal., 15: 540–554.
• Chuong, T. D. (2016) Nondifferentiable fractional semi-infinite multiobjective optimization problems. Operations Research Letters, 44(2): 260–266.
• Chuong, T. D. and Kim, D. S. (2014) Nonsmooth semi-infinite multiobjective optimization problems. J. Optim. Theory Appl., 160(3): 748–762.
• Deng, S. (1997) On approximate solutions in convex vector optimization. SIAM Journal on Control and Optimization, 35(6): 2128–2136.
• Dutta, J. and Vetrivel, V. (2001) On approximate minima in vector optimization. Numer. Funct. Anal. Optim., 22(7-8): 845–859.
• Goberna, M. A. and López Cerda, M. A. (1998) Linear Semi-Infinite Optimization. Wiley. Chichester.
• Guo, F. and Jiao, L. (2021) On solving a class of fractional semi-infinite polynomial programming problems. Comput. Optim. Appl., 80(2): 439–481.
• 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.
• 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.
• Jeyakumar, V. (2003) Characterizing set containments involving infinite convex constraints and reverse-convex constraints. SIAM J. Optim., 13(4): 947–959.
• 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.
• 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.
• 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.
• 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.
• 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.
• Kuroiwa, D. and Lee, G. M. (2012) On robust multiobjective optimization. Vietnam J. Math., 40: 305–317.
• Kutateladze, S. S. (1979) Convex ɛ-programming. Sov. Math., Dokl., 20: 391–393.
• 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.
• 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.
• 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.
• Liu, J. C. (1992) ɛ-duality theorem of nondifferentiable nonconvex multiobjective programming. J. Optim. Theory Appl., 74(3): 567–568.
• Liu, J. C. (1996) ɛ-Pareto optimality for nondifferentiable multiobjective programming via penalty function. J. Math. Anal. Appl., 198(1): 248— -61.
• Liu, J.-C. and Yokoyama, K. (1999) ɛ-optimality and duality for multiobjective fractional programming. Comput. Math. Appl., 37(8): 119–128.
• Loridan, P. (1984) ɛ-solutions in vector minimization problems. J. Optim. Theory Appl., 43: 265–276.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• White, D. J. (1986) Epsilon efficiency. J. Optim. Theory Appl., 49: 319–337.
• 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.