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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 57, 2008 - Issue 4
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Original Articles

Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives

Pages 593-605 | Received 16 Dec 2004, Accepted 31 Oct 2006, Published online: 23 May 2008

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Read on this site (9)

Tran Van Su & Do Van Luu. (2022) Second-Order Optimality Conditions for Strict Pareto Minima and Weak Efficiency for Nonsmooth Constrained Vector Equilibrium Problems. Numerical Functional Analysis and Optimization 43:15, pages 1732-1759.
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Tran Van Su & Do Van Luu. (2022) Higher-order efficiency conditions for constrained vector equilibrium problems. Optimization 71:9, pages 2613-2642.
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Bahareh Khazayel & Ali Farajzadeh. (2022) On the optimality conditions for D.C. vector optimization problems. Optimization 71:7, pages 2033-2045.
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Nguyen Le Hoang Anh. (2019) On Higher-Order Sensitivity Analysis of Parametric Henig Set-Valued Equilibrium Problems. Numerical Functional Analysis and Optimization 40:15, pages 1822-1839.
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Morteza Rahimi & Majid Soleimani-damaneh. (2018) Isolated efficiency in nonsmooth semi-infinite multi-objective programming. Optimization 67:11, pages 1923-1947.
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Do Van Luu. (2014) Higher-Order Efficiency Conditions Via Higher-Order Tangent Cones. Numerical Functional Analysis and Optimization 35:1, pages 68-84.
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Articles from other publishers (21)

Tran Van Su & Dinh Dieu Hang. (2022) Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems. Acta Mathematica Vietnamica 48:2, pages 321-341.
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Tran Van Su. (2021) Higher-Order Efficiency Conditions for Continuously Directional Differentiable Vector Equilibrium Problem with Constraints. Bulletin of the Iranian Mathematical Society 48:4, pages 1805-1828.
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Nguyen Le Hoang Anh, Nguyen Manh Truong Giang & Vo Duc Thinh. (2022) On optimality conditions for set-valued equilibrium problems. Computational and Applied Mathematics 41:1.
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Tran Van Su & Dinh Dieu Hang. (2021) Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints. Positivity 25:5, pages 1737-1760.
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Tran Van Su & Dinh Dieu Hang. (2020) Second-Order Necessary and Sufficient Optimality Conditions for Constrained Vector Equilibrium Problem with Applications. Bulletin of the Iranian Mathematical Society 47:5, pages 1337-1362.
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Elena Constantin. (2021) Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization. Journal of Global Optimization 80:1, pages 177-193.
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Tran Van Su. (2019) New Second-Order Optimality Conditions for Vector Equilibrium Problems with Constraints in Terms of Contingent Derivatives. Bulletin of the Brazilian Mathematical Society, New Series 51:2, pages 371-395.
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Guo-lin Yu & Tian-tian Gong. (2019) Higher-order Optimality Conditions and Duality for Approximate Solutions in Non-convex Set-valued Optimization. Acta Mathematicae Applicatae Sinica, English Series 35:3, pages 620-628.
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Aleksandra Stasiak. (2018) Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone. Journal of Applied Analysis 24:1, pages 45-54.
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Do Van Luu. (2017) Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems. Journal of Global Optimization 70:2, pages 437-453.
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Phan Quoc Khanh & Nguyen Minh Tung. (2018) Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization. SIAM Journal on Optimization 28:1, pages 820-848.
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Xiangyu Kong, GuoLin Yu & Wei Liu. (2017) Optimality for set-valued optimization in the sense of vector and set criteria. Journal of Inequalities and Applications 2017:1.
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Nguyen Le Hoang Anh & Phan Quoc Khanh. (2016) Higher-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization with nonsolid ordering cones. Positivity 21:3, pages 931-953.
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Nguyen Le Hoang Anh. (2015) Higher-order optimality conditions for strict and weak efficient solutions in set-valued optimization. Positivity 20:2, pages 499-514.
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Nguyen Le Hoang Anh. (2013) Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18:3, pages 449-473.
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Shengkun Zhu & Shengjie Li. (2013) Optimality conditions of strict minimality in optimization problems under inclusion constraints. Applied Mathematics and Computation 219:9, pages 4816-4825.
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S. J. Li, S. K. Zhu & X. B. Li. (2012) Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization. Journal of Optimization Theory and Applications 155:2, pages 534-557.
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El-Desouky Rahmo & Marcin Studniarski. (2012) Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives. Journal of Mathematical Analysis and Applications 393:1, pages 212-221.
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W. Y. Zhang, S. Xu & S. J. Li. (2012) Necessary Conditions for Weak Sharp Minima in Cone-Constrained Optimization Problems. Abstract and Applied Analysis 2012, pages 1-11.
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Bienvenido Jiménez, Vicente Novo & Miguel Sama. (2009) Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives. Journal of Mathematical Analysis and Applications 352:2, pages 788-798.
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Fabián Flores-Bazán & Bienvenido Jiménez. (2009) Strict Efficiency in Set-Valued Optimization. SIAM Journal on Control and Optimization 48:2, pages 881-908.
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