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Numerical Functional Analysis and Optimization Volume 22, 2001 - Issue 7-8
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Original Articles

ON APPROXIMATE MINIMA IN VECTOR OPTIMIZATION

J. Dutta Department d'Economia i d'Historia Economia, Universitat Autonoma de Barcelona, Bellaterra, 08193, SpainCorrespondence[email protected]
&
V. Vetrivel Department of Mathematics, Indian Institute of Technology, Madras, 600 036, India
Pages 845-859 | Published online: 17 Aug 2006

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P. K. Shukla, J. Dutta, K. Deb & P. Kesarwani. (2020) On a practical notion of Geoffrion proper optimality in multicriteria optimization. Optimization 69:7-8, pages 1513-1539.
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Mansi Dhingra & C. S. Lalitha. (2017) Approximate solutions and scalarization in set-valued optimization. Optimization 66:11, pages 1793-1805.
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M. Golestani, H. Sadeghi & Y. Tavan. (2017) Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems. Numerical Functional Analysis and Optimization 38:6, pages 683-704.
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K. Khaledian, E. Khorram & B. Karimi. (2015) Characterizing ϵ-properly efficient solutions. Optimization Methods and Software 30:3, pages 583-593.
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Ke Quan Zhao & Xin Min Yang. (2015) E-Benson proper efficiency in vector optimization. Optimization 64:4, pages 739-752.
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B.A. Ghaznavi-ghosoni, E. Khorram & M. Soleimani-damaneh. (2013) Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization. Optimization 62:6, pages 703-720.
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Ji-Hong Jia & Zhong-Fei Li. (2008) ε-Conjugate maps and ε-conjugate duality in vector optimization with set-valued maps. Optimization 57:5, pages 621-633.
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Deepali Gupta & Aparna Mehra. (2008) Two Types of Approximate Saddle Points. Numerical Functional Analysis and Optimization 29:5-6, pages 532-550.
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César Gutiérrez, Bienvenido Jiménez & Vicente Novo. (2006) ε-Pareto Optimality Conditions for Convex Multiobjective Programming via Max Function. Numerical Functional Analysis and Optimization 27:1, pages 57-70.
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Ke-Quan Zhao & Xin-Min Yang. (2014) $E$-PROPER SADDLE POINTS AND $E$-PROPER DUALITY IN VECTOR OPTIMIZATION WITH SET-VALUED MAPS. Taiwanese Journal of Mathematics 18:2.
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S. K. Mishra & B. B. Upadhyay. (2013) Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency. Positivity 17:4, pages 1071-1083.
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Rubén López. (2013) Variational convergence for vector-valued functions and its applications to convex multiobjective optimization. Mathematical Methods of Operations Research 78:1, pages 1-34.
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Ke-Quan Zhao, Xin-Min Yang & Jian-Wen Peng. (2013) WEAK E-OPTIMAL SOLUTION IN VECTOR OPTIMIZATION. Taiwanese Journal of Mathematics 17:4.
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Davinder Bhatia, Anjana Gupta & Pooja Arora. (2011) Optimality via generalized approximate convexity and quasiefficiency. Optimization Letters 7:1, pages 127-135.
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C. P. Liu, H. W. J. Lee & X. M. Yang. (2011) Optimality conditions and duality on approximate solutions in vector optimization with arcwise connectivity. Optimization Letters 6:8, pages 1613-1626.
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Y. Gao, S. H. Hou & X. M. Yang. (2011) Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems. Journal of Optimization Theory and Applications 152:1, pages 97-120.
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C. Gutiérrez, B. Jiménez & V. Novo. (2010) A generic approach to approximate efficiency and applications to vector optimization with set-valued maps. Journal of Global Optimization 49:2, pages 313-342.
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James J. Cochran, Louis A. CoxJr.Jr., Pinar Keskinocak, Jeffrey P. Kharoufeh & J. Cole SmithAlexander Engau. 2011. Wiley Encyclopedia of Operations Research and Management Science. Wiley Encyclopedia of Operations Research and Management Science.
C. Gutiérrez, R. López & V. Novo. (2010) Generalized -quasi-solutions in multiobjective optimization problems: Existence results and optimality conditions. Nonlinear Analysis: Theory, Methods & Applications 72:11, pages 4331-4346.
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Qiusheng Qiu & Xinmin Yang. (2009) Some properties of approximate solutions for vector optimization problem with set-valued functions. Journal of Global Optimization 47:1, pages 1-12.
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C. Gutiérrez, B. Jiménez & V. Novo. (2010) Optimality conditions via scalarization for a new -efficiency concept in vector optimization problems. European Journal of Operational Research 201:1, pages 11-22.
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Ying Gao, Xinmin Yang & HeungWingJoseph Lee. (2010) Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems. Journal of Inequalities and Applications 2010:1, pages 620928.
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A. Engau & M. M. Wiecek. (2007) Cone Characterizations of Approximate Solutions in Real Vector Optimization. Journal of Optimization Theory and Applications 134:3, pages 499-513.
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C. Gutiérrez, B. Jiménez & V. Novo. (2007) Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization. Journal of Optimization Theory and Applications 133:1, pages 49-64.
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Alexander Engau & Margaret M. Wiecek. (2007) Generating ε-efficient solutions in multiobjective programming. European Journal of Operational Research 177:3, pages 1566-1579.
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Igor V. Konnov, Dinh The Luc & Alexander M. RubinovCésar Gutiérrez, Bienvenido Jiménez & Vicente Novo. 2006. Generalized Convexity and Related Topics. Generalized Convexity and Related Topics 279 295 .
César Gutiérrez, Bienvenido Jiménez & Vicente Novo. (2006) On Approximate Solutions in Vector Optimization Problems Via Scalarization. Computational Optimization and Applications 35:3, pages 305-324.
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C. Gutiérrez, B. Jiménez & V. Novo. (2006) On Approximate Efficiency in Multiobjective Programming. Mathematical Methods of Operations Research 64:1, pages 165-185.
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César Gutiérrez, Bienvenido Jiménez & Vicente Novo. (2006) A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems. SIAM Journal on Optimization 17:3, pages 688-710.
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César Gutiérrez, Bienvenido Jiménez & Vicente Novo. 2006. Large-Scale Nonlinear Optimization. Large-Scale Nonlinear Optimization 173 184 .
Matthias Ehrgott & Margaret M. Wiecek. (2005) Saddle Points and Pareto Points in Multiple Objective Programming. Journal of Global Optimization 32:1, pages 11-33.
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