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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 60, 2011 - Issue 5
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Original Articles

On some Fermat rules for set-valued optimization problems

M. Durea Faculty of Mathematics, Al. I. Cuza University, Bd. Carol I, nr. 11, 700506 – Iaşi, RomaniaCorrespondence[email protected]
&
R. Strugariu Department of Mathematics, Gh. Asachi Technical University, Bd. Carol I, nr. 11, 700506 – Iaşi, Romania
Pages 575-591 | Received 28 Apr 2009, Accepted 20 Nov 2009, Published online: 11 Nov 2010

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Elena-Andreea Florea & Diana Maxim. (2021) Directional openness for epigraphical mappings and optimality conditions for directional efficiency. Optimization 70:2, pages 321-344.
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Marius Durea. (2020) Optimality Conditions for Approximate Pareto Minimality. Numerical Functional Analysis and Optimization 41:8, pages 883-900.
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Marius Durea & Radu Strugariu. (2017) Generalized penalization and maximization of vectorial nonsmooth functions. Optimization 66:6, pages 903-915.
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Marius Durea, Marian Panţiruc & Radu Strugariu. (2016) Minimal time function with respect to a set of directions: basic properties and applications. Optimization Methods and Software 31:3, pages 535-561.
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M. Ait Mansour & H. Riahi. (2015) Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming. Optimization 64:4, pages 771-797.
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Articles from other publishers (25)

Marius Durea & Radu Strugariu. (2022) Directional derivatives and subdifferentials for set-valued maps applied to set optimization. Journal of Global Optimization 85:3, pages 687-707.
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Mohamed Ait Mansour, Marius Durea & Hassan Riahi. (2021) Strict directional solutions in vectorial problems: necessary optimality conditions. Journal of Global Optimization 82:1, pages 119-138.
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Marius Durea, Diana Maxim & Radu Strugariu. (2021) Metric Inequality Conditions on Sets and Consequences in Optimization. Journal of Optimization Theory and Applications 189:3, pages 744-771.
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Marius Durea & Radu Strugariu. (2020) On the sensitivity of Pareto efficiency in set-valued optimization problems. Journal of Global Optimization 78:3, pages 581-596.
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Teodor Chelmuş, Marius Durea & Elena-Andreea Florea. (2019) Directional Pareto Efficiency: Concepts and Optimality Conditions. Journal of Optimization Theory and Applications 182:1, pages 336-365.
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Elena-Andreea Florea. (2018) Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting. Journal of Optimization Theory and Applications 178:1, pages 94-118.
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Marius Durea & Elena-Andreea Florea. (2017) A Study of Generalized Vector Variational Inequalities via Vector Optimization Problems. Vietnam Journal of Mathematics 46:1, pages 33-52.
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Marius Durea, Radu Strugariu & Christiane Tammer. (2017) On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization. Journal of Optimization Theory and Applications 175:3, pages 738-763.
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Marius Durea, Marian Panţiruc & Radu Strugariu. (2017) A New Type of Directional Regularity for Mappings and Applications to Optimization. SIAM Journal on Optimization 27:2, pages 1204-1229.
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Marius Durea, Radu Strugariu & Christiane Tammer. (2014) On set-valued optimization problems with variable ordering structure. Journal of Global Optimization 61:4, pages 745-767.
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Andreas H. Hamel, Frank Heyde, Andreas Löhne, Birgit Rudloff & Carola Schrage. 2015. Set Optimization and Applications - The State of the Art. Set Optimization and Applications - The State of the Art 65 141 .
Marius Durea & Radu Strugariu. (2013) Scalarization of constraints system in some vector optimization problems and applications. Optimization Letters 8:7, pages 2021-2037.
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Marius Apetrii, Marius Durea & Radu Strugariu. (2014) A new penalization tool in scalar and vector optimizations. Nonlinear Analysis: Theory, Methods & Applications 107, pages 22-33.
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Marius Durea, Van Ngai Huynh, Huu Tron Nguyen & Radu Strugariu. (2014) Metric regularity of composition set-valued mappings: Metric setting and coderivative conditions. Journal of Mathematical Analysis and Applications 412:1, pages 41-62.
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Huynh Van Ngai, Nguyen Huu Tron & Michel Théra. (2013) Metric Regularity of the Sum of Multifunctions and Applications. Journal of Optimization Theory and Applications 160:2, pages 355-390.
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Marius Durea & Radu Strugariu. (2012) Chain rules for linear openness in metric spaces and applications. Mathematical Programming 143:1-2, pages 147-176.
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X. J. Long, X. B. Li & J. Zeng. (2012) Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems. Optimization Letters 7:8, pages 1847-1856.
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Marius Durea, Radu Strugariu & Christiane Tammer. (2013) Scalarization in Geometric and Functional Vector Optimization Revisited. Journal of Optimization Theory and Applications 159:3, pages 635-655.
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Marius Durea, Huu Tron Nguyen & Radu Strugariu. (2013) Metric regularity of epigraphical multivalued mappings and applications to vector optimization. Mathematical Programming 139:1-2, pages 139-159.
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Marius Apetrii, Marius Durea & Radu Strugariu. (2012) On Subregularity Properties of Set-Valued Mappings. Set-Valued and Variational Analysis 21:1, pages 93-126.
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S. K. Zhu, S. J. Li & X. W. Xue. (2012) Strong Fermat Rules for Constrained Set-Valued Optimization Problems on Banach Spaces. Set-Valued and Variational Analysis 20:4, pages 637-666.
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Truong Q. Bao & Boris S. Mordukhovich. (2012) Sufficient conditions for global weak Pareto solutions in multiobjective optimization. Positivity 16:3, pages 579-602.
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M. Durea & R. Strugariu. (2011) On parametric vector optimization via metric regularity of constraint systems. Mathematical Methods of Operations Research 74:3, pages 409-425.
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M. Durea & R. Strugariu. (2011) Existence conditions for generalized vector variational inequalities. Annals of Operations Research 191:1, pages 255-262.
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M. Durea & R. Strugariu. (2010) Optimality conditions in terms of Bouligand derivatives for Pareto efficiency in set-valued optimization. Optimization Letters 5:1, pages 141-151.
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