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Optimality conditions for mathematical programming problem with equilibrium constraints in terms of tangential subdifferentiable | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 تیر 1404 اصل مقاله (599.7 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30232.2375 | ||
| نویسندگان | ||
| Rishabh Pandey1؛ Yogendra Pandey2؛ vinay singh* 1 | ||
| 1Department of Mathematics, National Institute of Technology Mizoram, Aizawl, 796012, Mizoram, India | ||
| 2Department of Mathematics, Satish Chandra College, Ballia, 277001, Uttar Pradesh, India | ||
| چکیده | ||
| The aim of this article is to develop necessary and sufficient optimality conditions for nonsmooth mathematical programs with equilibrium constraints $(\mathcal{MPEC})$. We introduce a nonsmooth variant of the standard $\partial^{T}$-Abadie constraint qualification ($\partial^{T}$-$ACQ(\mathfrak{B}_1, \mathfrak{B}_2)$) and propose $\partial^{T}$-generalized alternatively stationary conditions using the tangential subdifferential framework. Building on these new conditions, we derive first-order optimality criteria under $\partial^{T}$-$ACQ(\mathfrak{B}_1, \mathfrak{B}_2)$. Additionally, we establish sufficient optimality conditions within a framework of generalized convexity assumptions. The effectiveness and applicability of these conditions are demonstrated through several examples. | ||
| کلیدواژه‌ها | ||
| MPEC؛ disjoint bipartitions؛ GA-stationary point | ||
| مراجع | ||
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[1] A. Ansari Ardali, N. Movahedian, and S. Nobakhtian, Optimality conditions for nonsmooth mathematical programs with equilibrium constraints, using convexificators, Optimization 65 (2016), no. 1, 67–85. https://doi.org/10.1080/02331934.2014.987776
[2] B.T. Baumrucker, J.G. Renfro, and L.T. Biegler, MPEC problem formulations and solution strategies with chemical engineering applications, Comput. Chem. Eng. 32 (2008), no. 12, 2903–2913. https://doi.org/10.1016/j.compchemeng.2008.02.010
[3] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, NY, USA, 1983.
[4] M. L. Flegel and C. Kanzow, On the guignard constraint qualification for mathematical programs with equilibrium constraints, Optimization 54 (2005), no. 6, 517–534. https://doi.org/10.1080/02331930500342591
[5] M.L. Flegel, Constraint qualifications and stationarity concepts for mathematical programs with equilibrium constraints, Doctoral dissertation, Universität Würzburg, 2005.
[6] M.L. Flegel and C. Kanzow, A fritz john approach to first order optimality conditions for mathematical programs with equilibrium constraints, Optimization 52 (2003), no. 3, 277–286. https://doi.org/10.1080/0233193031000120020
[7] M.L. Flegel and C. Kanzow, Abadie-type constraint qualification for mathematical programs with equilibrium constraints, J. Optim. Theory Appl. 124 (2005), no. 3, 595–614. https://doi.org/10.1007/s10957-004-1176-x
[8] N.A. Gadhi and M. Ohda, Optimality conditions for MPECs in terms of directional upper convexifactors, RAIRO Oper. Res. 56 (2022), no. 6, 4303–4316. https://doi.org/10.1051/ro/2022203
[9] N.A. Gadhi and M. Ohda, Applying tangential subdifferentials in bilevel optimization, Optimization 73 (2024), no. 9, 2919–2932. https://doi.org/10.1080/02331934.2023.2231501 [10] O. Güler, Separation of convex sets, pp. 141–173, Springer New York, New York, NY, 2010.
[11] Y. Guo, G. Ye, W. Liu, D. Zhao, and S. Treanţǎ, Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity, Chaos Solit.Fractals. 174 (2023), Article ID: 113834 https://doi.org/10.1016/j.chaos.2023.113834
[12] M. Jennane and E.M. Kalmoun, On nonsmooth multiobjective semi-infinite programming with switching constraints using tangential subdifferentials, Stat., optim. inf. comput. 11 (2023), no. 1, 22–28. https://doi.org/10.19139/soic-2310-5070-1704
[13] P.Q. Khanh and L.T. Tung, On optimality conditions and duality for multiobjective optimization with equilibrium constraints, Positivity 27 (2023), no. 4, Article ID: 49 https://doi.org/10.1007/s11117-023-01001-8
[14] B. Kohli, Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints, RAIRO Oper. Res. 53 (2019), no. 5, 1617–1632. https://doi.org/10.1051/ro/2018084
[15] C. Lemaréchal, An introduction to the theory of nonsmooth optimization, Optimization 17 (1986), no. 6, 827–858. https://doi.org/10.1080/02331938608843204 [16] Z.Q. Luo, J.S. Pang, and D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, 1996.
[17] D.V. Luu and D.D. Hang, On efficiency conditions for nonsmooth vector equilibrium problems with equilibrium constraints, Numer. Funct. Anal. Optim. 36 (2015), no. 12, 1622–1642. https://doi.org/10.1080/01630563.2015.1078813
[18] J.E. Martínez-Legaz, Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints, Optim. Lett. 9 (2015), no. 5, 1017–1023. https://doi.org/10.1007/s11590-014-0822-y
[19] F. Mashkoorzadeh, N. Movahedian, and S. Nobakhtian, Robustness in nonsmooth nonconvex optimization problems, Positivity 25 (2021), no. 2, 701–729. https://doi.org/10.1007/s11117-020-00783-5
[20] F. Mashkoorzadeh, N. Movahedian, and S. Nobakhtian, The DTC (difference of tangentially convex functions) programming: optimality conditions, Top 30 (2022), no. 2, 270–295. https://doi.org/10.1007/s11750-021-00615-z
[21] P. Michel and J.P. Penot, A generalized derivative for calm and stable functions, Differ. Integral Equ. 5 (1992), 433–454. https://doi.org/10.57262/die/1371043981
[22] Y. Pandey and S.K. Mishra, Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators, Ann. Oper. Res. 269 (2018), no. 2, 549–564. https://doi.org/10.1007/s10479-017-2422-6
[23] B.N. Pshenichnyi, Necessary Conditions for An Extremum, Marcel Dekker Inc, 1971.
[24] A.U. Raghunathan, M.S. Diaz, and L.T. Biegler, An MPEC formulation for dynamic optimization of distillation operations, Comput. Chem. Eng. 28 (2004), no. 10, 2037–2052. https://doi.org/10.1016/j.compchemeng.2004.03.015
[25] N. Sisarat and R. Wangkeeree, Characterizing the solution set of convex optimization problems without convexity of constraints, Optim. Lett. 14 (2020), no. 5, 1127–1144. https://doi.org/10.1007/s11590-019-01397-x
[26] S. Treanţǎ, A.O. Bibic, and S.M. Bibic, Efficiency criteria for multicost variational models driven by h-type i functionals, J. Multi-Crit. Decis. Anal. 31 (2024), no. 5-6, Article ID: e70004. https://doi.org/10.1002/mcda.70004
[27] S. Treanţǎ and M.A. Dragu, Euler–lagrange equation for gradient-type Lagrangian and related conservation laws, J. Appl. Math. Comput. 71 (2024), no. 2, 1565–1579. https://doi.org/10.1007/s12190-024-02303-0
[28] S. Treanţǎ, C.F. Marghescu, and B.C. Joshi, Efficiency criteria driven by dual models for multiple cost control problems, Numer. Algebra Control Optim. 15 (2024), no. 3, 750–765. https://doi.org/10.3934/naco.2024038
[29] S. Treanţǎ, V. Singh, and S.K. Mishra, Reciprocal solution existence results for a class of vector variational control inequalities with application in physics, J. Comput. Appl. Math. 461 (2025), Article ID: 116461 https://doi.org/10.1016/j.cam.2024.116461
[30] I.P. Tripathi and M.A. Arora, Fractional semi-infinite programming problems: optimality conditions and duality via tangential subdifferentials, Comput. Appl. Math. 43 (2024), no. 6, Article ID: 388 https://doi.org/10.1007/s40314-024-02912-2
[31] L.T. Tung, Strong Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming via tangential subdifferential, RAIRO Oper. Res. 52 (2018), no. 4-5, 1019–1041. https://doi.org/10.1051/ro/2018020
[32] L.T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming via tangential subdifferentials, Numer. Funct. Anal. Optim. 41 (2020), no. 6, 659–684. https://doi.org/10.1080/01630563.2019.1667826
[33] J.J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints, J. Math. Anal. Appl. 307 (2005), 350–369. https://doi.org/10.1016/j.jmaa.2004.10.032 | ||
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