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Heiatian Naeini, Parastoo, Rezaee, Ahmad. (1405). An Invex Active-Slater Test for Clarke-MFCQ in Nonsmooth Multiobjective Optimization. فصلنامه علمی زیست فناوری گیاهان زراعی, (), -. doi: 10.30473/coam.2026.77019.1395
Parastoo Heiatian Naeini; Ahmad Rezaee. "An Invex Active-Slater Test for Clarke-MFCQ in Nonsmooth Multiobjective Optimization". فصلنامه علمی زیست فناوری گیاهان زراعی, , , 1405, -. doi: 10.30473/coam.2026.77019.1395
Heiatian Naeini, Parastoo, Rezaee, Ahmad. (1405). 'An Invex Active-Slater Test for Clarke-MFCQ in Nonsmooth Multiobjective Optimization', فصلنامه علمی زیست فناوری گیاهان زراعی, (), pp. -. doi: 10.30473/coam.2026.77019.1395
Heiatian Naeini, Parastoo, Rezaee, Ahmad. An Invex Active-Slater Test for Clarke-MFCQ in Nonsmooth Multiobjective Optimization. فصلنامه علمی زیست فناوری گیاهان زراعی, 1405; (): -. doi: 10.30473/coam.2026.77019.1395

An Invex Active-Slater Test for Clarke-MFCQ in Nonsmooth Multiobjective Optimization

Control and Optimization in Applied Mathematics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 12 شهریور 1405    اصل مقاله (359.73 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2026.77019.1395
نویسندگان
Parastoo Heiatian Naeini* ؛ Ahmad Rezaee
Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran
چکیده
We consider a finite-dimensional multiobjective optimization problem with locally Lipschitz objective functions and finitely many locally Lipschitz inequality constraints. We formulate an active-set Slater test in which σxˆ is selected from a structurally restricted admissible class or selection rule Σ(ψ, xˆ) prescribed before testing the qualification, rather than constructed from an MFCQ direction. Pointwise (σxˆ, rj)-invex inequalities with rj ≥ 0 imply the Clarke–Mangasarian–Fromovitz constraint qualification (ClarkeMFCQ). Standard maximum-function and normal-cone arguments then yield normalized Clarke–KKT multipliers at locally weakly efficient solutions, positive objective multipliers for positive weighted-sum solutions, and a perturbed-KKT inclusion at locally isolated efficient solutions. If Σ(ψ, xˆ) contains every locally Lipschitz map, the test is equivalent to Clarke-MFCQ. A nonsmooth nonconvex example illustrates the assumptions and multiplier inclusions.

تازه های تحقیق
  • An active σ,r-Slater condition is proven sufficient for Clarke-MFCQ.
  • The condition is proven equivalent to Clarke-MFCQ over an unrestricted class.
  • Fritz–John and normalized KKT conditions are derived for weakly efficient points.
  • Positive weighted-sum solutions are shown to admit strictly positive multipliers.
  • A regularity-free normal-cone estimate yields a perturbed-KKT condition.
کلیدواژه‌ها
Nonsmooth multiobjective optimization؛ Clarke subdifferential؛ constraint qualification؛ Invexity؛ KKT conditions؛ Isolated efficient solution
مراجع

[1] Antczak, T. (2002). “Lipschitz r-invex functions and nonsmooth programming”. Numerical Functional Analysis and Optimization, 23, 265–283. https://doi.org/10.1081/ NFA-120006693

[2] Audet, C., Dennis, J.E., Jr. (2006). “Mesh adaptive direct search algorithms for constrained optimization”. SIAM Journal on Optimization, 17, 188–217. https://doi.org/ 10.1137/040603371

[3] Clarke, F.H., Ledyaev, Y.S., Stern, R.J., Wolenski, R.R. (1998). “Nonsmooth Analysis and Control Theory”. Graduate Texts in Mathematics, Vol. 178, Springer, New York.

[4] Clarke, F.H. (1990). “Optimization and Nonsmooth Analysis”. Classics in Applied Mathematics, Vol. 5, SIAM, Philadelphia. https://doi.org/10.1137/1.9781611971309

[5] Caristi, G., Kanzi, N., Soleimani-Damaneh, M. (2018). “On gap functions for nonsmooth multiobjective optimization problems”. Optimization Letters, 12, 273–286. https://doi.org/10.1007/s11590-017-1110-4

[6] Ehrgott, M. (2005). “Multicriteria Optimization”. Springer, Berlin.

[7] Giorgi, G., Guerraggio, A., Thierfelder, J. (2004). “Mathematics of Optimization: Smooth and Nonsmooth Cases”. Elsevier, Amsterdam.

[8] Goberna, M.A., Kanzi, N. (2017). “Optimality conditions in convex multiobjective SIP”. Mathematical Programming, 164, 167–191. https://doi.org/10.1007/ s10107-016-1081-8

[9] Guerraggio, A., Molho, E., Zaffaroni, A. (1994). “On the notion of proper efficiency in vector optimization”. Journal of Optimization Theory and Applications, 82, 1–21. https: //doi.org/10.1007/BF02191776

[10] Habibi, S., Kanzi, N., Ebadian, A. (2020). “Weak Slater qualification for nonconvex multiobjective semi-infinite programming”. Iranian Journal of Science and Technology, Transactions A: Science, 44, 417–424. https://doi.org/10.1007/s40995-020-00835-1

[11] Hanson, M.A. (1981). “On sufficiency of the Kuhn–Tucker conditions”. Journal of Mathematical Analysis and Applications, 80, 545–550. https://doi.org/10.1016/ 0022-247X(81)90123-2

[12] Hiriart-Urruty, J.B., Lemarechal, C. (1993). “Convex Analysis and Minimization Algorithms I: Fundamentals”. Springer, Berlin.

[13] Jeyakumar, V. (1988). “Equivalence of saddle-points and optima, and duality for a class of nonsmooth non-convex problems”. Journal of Mathematical Analysis and Applications, 130, 334–343. https://doi.org/10.1016/0022-247X(88)90309-5

[14] Kanzi, N. (2015). “Karush–Kuhn–Tucker types optimality conditions for non-smooth semi-infinite vector optimization problems”. Journal of Mathematical Extension, 9, 45– 56.

[15] Kanzi, N. (2015). “On strong KKT optimality conditions for multiobjective semi-infinite programming problems with Lipschitzian data”. Optimization Letters, 9, 1121–1129. https://doi.org/10.1007/s11590-014-0801-3

[16] Kanzi, N., Shaker Ardekani, J., Caristi, G. (2018). “Optimality, scalarization and duality in linear vector semi-infinite programming”. Optimization, 67, 523–536. https://doi. org/10.1080/02331934.2018.1436158

[17] Kanzi, N., Caristi, G., Sadeghieh, A. (2019). “Optimality conditions for semi-infinite programming problems involving generalized convexity”. Optimization Letters, 13, 113–126. https://doi.org/10.1007/s11590-018-1278-0

[18] Kanzi, N., Nobakhtian, S. (2017). “Nonsmooth multiobjective semi-infinite problems with mixed constraints”. Pacific Journal of Optimization, 13, 43–53. https://doi.org/10.48550/arXiv.1606.08641

[19] Kim, D.S., Schaible, S. (2004). “Optimality and duality for invex nonsmooth multiobjective programming problems”. Optimization, 53, 165–176. https://doi.org/10.1080/ 0233193042000209435

[20] Laha, V., Dwivedi, A. (2024). “On approximate strong KKT points of nonsmooth interval-valued multiobjective optimization problems using convexificators”. The Journal of Analysis, 32, 219–242. https://doi.org/10.1007/s41478-023-00621-3

[21] Li, X.F., Dong, J.L., Liu, Q.H. (1997). “Lipschitz B-vex functions and nonsmooth programming”. Journal of Optimization Theory and Applications, 93, 557–574. https://doi.org/10.1023/A:1022678920437

[22] Lee, G.M. (1994). “Nonsmooth invexity in multiobjective programming”. Journal of Information and Optimization Sciences, 15, 127–136. https://doi.org/10.1080/ 02522667.1994.10699173

[23] Luc, D.T. (1989). “Theory of Vector Optimization”. Lecture Notes in Economics and Mathematical Systems, Vol. 319, Springer, Berlin.

[24] Rockafellar, R.T. (1970). “Convex Analysis”. Princeton Mathematical Series, Vol. 28, Princeton University Press, Princeton, NJ.

[25] Reiland, T.W. (1989). “Generalized invexity for nonsmooth vector-valued mappings”. Numerical Functional Analysis and Optimization, 10, 1191–1202. https://doi.org/10. 1080/01630568908816352

[26] Reiland, T.W. (1990). “Nonsmooth invexity”. Bulletin of the Australian Mathematical Society, 42, 437–446. https://doi.org/10.1017/S0004972700028604

[27] Rezaee, A. (2019). “Characterization of isolated efficient solutions in nonsmooth multiobjective semi-infinite programming”. Iranian Journal of Science and Technology, Transactions A: Science, 43, 1835–1839. https://doi.org/10.1007/s40995-018-0637-2

[28] Rimpi, Lalitha, C.S. (2023). “Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints”. Optimization, 72, 2019–2038. https://doi.org/10.1080/02331934.2022.2045987

[29] Rockafellar, R.T., Wets, J.B. (1998). “Variational Analysis”. Springer, Berlin.

[30] Sachan, P., Laha, V., Anshika (2026). “First and second order optimality conditions for nonsmooth multiobjective problems with equilibrium constraints”. Journal of Optimization Theory and Applications, 208, Article 15. https://doi.org/10.1007/s10957-025-02853-8

[31] Sadeghieh, A., Kanzi, N., Caristi, G., Barilla, D. (2022). “Stationarity for nonsmooth multiobjective problems with vanishing constraints”. Journal of Global Optimization, 82, 929–949. https://doi.org/10.1007/s10898-021-01030-1

[32] Sawaragi, Y., Nakayama, H., Tanino, T. (1985). “Theory of Multiobjective Optimization”. Mathematics in Science and Engineering, Vol. 176, Academic Press, Orlando.

[33] Shaker Ardakani, J., Farahmand Rad, S.H., Kanzi, N., Ardabili, P. (2019). “Necessary stationary conditions for multiobjective optimization problems with nondifferentiable convex vanishing constraints”. Iranian Journal of Science and Technology, Transactions A: Science, 43, 2913–2919. https://doi.org/10.1007/s40995-019-00768-4

[34] Upadhyay, B.B., Ghosh, A., Stancu-Minasian, I.M., Rusu-Stancu, A.M. (2026). “Constraint qualifications and optimality criteria for nonsmooth multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds”. Axioms, 15, Article 40. https://doi.org/10.3390/axioms15010040

[35] Vial, J.P. (1983). “Strong and weak convexity of sets and functions”. Mathematics of Operations Research, 8, 231–259. https://doi.org/10.1287/moor.8.2.231

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