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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 25, 1992 - Issue 1
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Original Articles

On the notion of tangent cone in mathematical programming

G. Giorgi Department of Management Science, University of Pauia, Italy
,
A. Guerraggio Department of Management Science, University of Pauia, Italy
&
A. Guerraggio Department of Management Science, University of Pauia, Italy
Pages 11-23 | Published online: 20 Mar 2007

Citations (23)

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Read on this site (4)

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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Tran Van Su & Nguyen Duc Hien. (2021) Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications. Optimization 70:1, pages 121-148.
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Do Van Luu. (2008) Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives. Optimization 57:4, pages 593-605.
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G. Giorgi & A. Guerraggio. (2002) Characterizations, comparisons, algebraic and topological properties of tangent cones. Journal of Statistics and Management Systems 5:1-3, pages 275-294.
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Articles from other publishers (19)

Giorgio Giorgi, Bienvenido Jiménez & Vicente Novo. (2023) Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results. Decisions in Economics and Finance 46:2, pages 355-377.
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Giorgio Giorgi, Bienvenido Jiménez & Vicente NovoGiorgio Giorgi, Bienvenido Jiménez & Vicente Novo. 2023. Basic Mathematical Programming Theory. Basic Mathematical Programming Theory 317 382 .
Karla L. Cortez & Javier F. Rosenblueth. (2021) The Supporting Role of the Mangasarian-Fromovitz Constraint Qualification in Calculus of Variations. Journal of Dynamical and Control Systems 28:3, pages 493-504.
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Tran Van Su & Dinh Dieu Hang. (2021) Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints. 4OR 20:1, pages 105-137.
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Bennet Gebken, Sebastian Peitz & Michael Dellnitz. (2019) On the hierarchical structure of Pareto critical sets. Journal of Global Optimization 73:4, pages 891-913.
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Akhtar A. Khan, Christiane Tammer & Constantin ZălinescuAkhtar A. Khan, Christiane Tammer & Constantin Zălinescu. 2015. Set-valued Optimization. Set-valued Optimization 109 211 .
Regina S. Burachik & M. M. Rizvi. (2014) Proper Efficiency and Proper Karush–Kuhn–Tucker Conditions for Smooth Multiobjective Optimization Problems. Vietnam Journal of Mathematics 42:4, pages 521-531.
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Giorgio Giorgi. (2013) A Note on the Guignard Constraint Qualification and the Guignard Regularity Condition in Vector Optimization. Applied Mathematics 04:04, pages 734-740.
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Ziteng Wang, Shu-Cherng Fang & Wenxun Xing. (2013) On constraint qualifications: Motivation, design and inter-relations. Journal of Industrial & Management Optimization 9:4, pages 983-1001.
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Roberto Andreani, Gabriel Haeser, María Laura Schuverdt & Paulo J. S. Silva. (2011) A relaxed constant positive linear dependence constraint qualification and applications. Mathematical Programming 135:1-2, pages 255-273.
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G. Giorgi, B. Jiménez & V. Novo. (2013) An overview of second order tangent sets and their application to vector optimization. SeMA Journal 52:1, pages 73-96.
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B. Jiménez & V. Novo. (2006) Characterization of the Cone of Attainable Directions. Journal of Optimization Theory and Applications 131:3, pages 493-499.
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. 2004. Mathematics of Optimization. Mathematics of Optimization 359 457 .
. 2004. Mathematics of Optimization. Mathematics of Optimization 201 358 .
Bienvenido Jiménez. (2002) Strict Efficiency in Vector Optimization. Journal of Mathematical Analysis and Applications 265:2, pages 264-284.
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T. D. Phuong, P. H. Sach & N. D. Yen. (1995) Strict lower semicontinuity of the level sets and invexity of a locally Lipschitz function. Journal of Optimization Theory and Applications 87:3, pages 579-594.
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Giorgio Giorgi. 1995. Nonlinear and Convex Analysis in Economic Theory. Nonlinear and Convex Analysis in Economic Theory 53 66 .
A. Guerraggio, E. Molho & A. Zaffaroni. (1994) On the notion of proper efficiency in vector optimization. Journal of Optimization Theory and Applications 82:1, pages 1-21.
Crossref
G. Giorgi & A. Guerraggio. 1994. Generalized Convexity. Generalized Convexity 171 185 .

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