Sequential approximate optimality conditions for a constrained convex vector minimization problem and application to multiobjective fractional programming problem

Iranian Journal of Numerical Analysis and Optimization

مقاله 11، دوره 15، Issue 2 - شماره پیاپی 33، شهریور 2025، صفحه 676-703   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90229.1534

نویسندگان

A. Ed-dahdah^* ؛ M. Laghdir؛ M. Echchaabaoui؛ M. Mabrouk

Department of Mathematics, Faculty of Sciences, University of Chouaib Doukkali, El jadida, Morocco.

چکیده

The aim of this paper is to establish sequential necessary and sufficient approximate optimality conditions for a constrained convex vector mini-mization problem without any constraint qualifications, characterizing the approximate proper and weak efficient solutions. The constraints are de-scribed by mappings taking values in different preorder vector spaces. Our approach is based essentially on the sequential approximate subdifferential calculus rule for the sums of a finite family of cone convex mappings. To illustrate our main result, an application to multiobjective fractional pro-gramming problem is given. Finally, we present an important subclass of such problems showing the applicability of the obtained conditions.

کلیدواژه‌ها

Vector optimization؛ Approximate Pareto subdifferential of con-vex mappings؛ Sequential approximate optimality conditions

مراجع

[1] Bai, F.S., Wu, Z.Y. and Zhu, D.L. Sequential Lagrange multiplier con-dition for ε-optimal solution in convex programming, Optimization. 57 (2008), 669–680.
[2] Bard, J.F. Practical Bilevel Optimization: Algorithms and Applications, Springer Science and Business Media. 30, 2013.
[3] Boţ, R.I., Csetnek, E.R. and Wanka, G. Sequential optimality conditions for composed convex optimization problems, J. Math. Anal. Appl. 342(2) (2008), 1015–1025.
[4] Dinkelbach, W. On nonlinear fractional programming, Manage. Sci. 13 (1967), 492–498.
[5] EL Maghri, M. Pareto-Fenchel ε-subdifferential sum rule ε-efficiency, Optim. Lett. 6(4) (2012), 763–781.
[6] El Maghri, M. Pareto-Fenchel ε-subdifferential composition rule and ε-efficiency, Numer. Funct. Anal. Optim. 35(1) (2014), 1–19.
[7] El Maghri, M. and Laghdir, M. Pareto subdifferential calculus for convex vector mappings and applications to vector optimization, SIAM J. Optim. 19 (2008), 1970–1994.
[8] Jeyakumar, V., Lee, G.M. and Dinh, N. New sequential Lagrange mul-tiplier conditions characterizing optimality without constraint qualifica-tions for convex programs, SIAM J. Optim. 14(2) (2003), 534–547.
[9] Jeyakumar, V., Lee, G.M. and Dinh, N. Liberating the subgradient op-timality conditions from constraint qualifications, J. Glob. Optim. 36 (2006), 127–137.
[10] Kim, M.H., Kim, G.S. and Lee, G.M. On ε-optimality conditions for multiobjective fractional optimization problems, Fixed Point Theory Appl.(2011), 1–13.
[11] Kohli, B. Sequential optimality conditions for multiobjective fractional programming problems, Math Sci. 8(2) (2014), 128.

[12] Luhandjula, M.K. Fuzzy approach for multiple objective linear fractional programming problems, Fuzzy Sets Syst. 13(1) (1984), 11–23.
[13] Moustaid, M.B., Laghdir, M., Dali, I. and Rikouane, A. Sequential op-timality conditions for multi objective fractional programming problems via sequential subdifferential calculus, Le Matematiche. 76(1) (2021), 79–96.
[14] Moustaid, M.B., Rikouane, A., Dali, I. and Laghdir, M. Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brndsted-Rockafellar approximate subdifferential, Rend. Circ. Mat. Palermo, II. Ser. (2022), 337–754.
[15] Stancu-Minasian, I.M. Fractional programming : Theory, Methodsand Applica- tions, Springer Science and Business Media. 409, 2012.
[16] Stancu-Minasian, I.M. A ninth bibliography of fractional programming, Optimization. 68(11) (2019) 2125–2169.
[17] Sun, G.Z. An economic approach to some classical theorem in optimiza-tion theory, Optim. Lett. 2(2) (2008), 281–286.
[18] Sun, X.K., Long, X.J. and Chai, Y. Sequential optimality conditions for fractional optimization with applications to vector optimization, J Optim. Theory. Appl. 164(2) (2015), 479–499.
[19] Thibault, L. Sequential convex subdifferential calculus and sequential Lagrange multipliers, SIAM J. Control. Optim. 35(4) (1997), 1434–1444.
[20] Zappone, A. and Jorswieck, E. Energy efficiency in wireless networks via fractional programming theory, Found. Trends Commun. Inf. Theory, 11 (2015), 185–396.