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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 60, 2011 - Issue 12
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Original Articles

A unified vector optimization problem: complete scalarizations and applications

Fabián Flores-Bazán Departamento de Ingeniería Matemática, CIMA, Universidad de Concepción, Casilla 160-C, Concepción, ChileCorrespondence[email protected]
&
Elvira Hernández Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, 28040, Madrid, Spain
Pages 1399-1419 | Received 24 May 2011, Accepted 10 Nov 2011, Published online: 14 Dec 2011

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Fabián Flores-Bazán & Cristian Vera. (2022) Efficiency in quasiconvex multiobjective nondifferentiable optimization on the real line. Optimization 71:2, pages 285-307.
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M. Ghaznavi, F. Akbari & E. Khorram. (2021) Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization. Optimization Methods and Software 36:2-3, pages 627-652.
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Petra Weidner. (2020) Scalarization in vector optimization with arbitrary domination sets. Optimization 69:7-8, pages 1731-1750.
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Kequan Zhao, Guangya Chen & Xinmin Yang. (2015) Approximate proper efficiency in vector optimization. Optimization 64:8, pages 1777-1793.
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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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Articles from other publishers (41)

Liu Caiping & Yang Xinmin. (2023) bmE-properly efficient elements of vector optimization problems and their scalarization. SCIENTIA SINICA Mathematica.
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H. T. H. Diem, S. Jafari, P. Q. Khanh & S. Moradi. (2022) Conditions for solutions, their globality, and their duality relations in vector optimization with relaxed quasiconvexity. Positivity 26:3.
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Shiva Kapoor & C.S. Lalitha. (2022) Continuity and closedness of constraint and solution set mappings in unified parametric semi-infinite vector optimization. Journal of Mathematical Analysis and Applications 506:2, pages 125648.
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Ying Gao & Liping Tang. (2022) Gerstewitz nonlinear scalar functional and the applications in vector optimization problems. Filomat 36:16, pages 5615-5629.
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Khushboo & C.S. Lalitha. (2021) Scalarization and convergence in unified set optimization. RAIRO - Operations Research 55:6, pages 3603-3616.
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Shiva Kapoor & C. S. Lalitha. (2021) Essential stability in unified vector optimization. Journal of Global Optimization 80:1, pages 161-175.
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Le Phuoc Hai. (2020) Ekeland variational principles involving set perturbations in vector equilibrium problems. Journal of Global Optimization 79:3, pages 733-756.
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Khushboo & C. S. Lalitha. 2021. Optimization, Variational Analysis and Applications. Optimization, Variational Analysis and Applications 1 17 .
Adrian Carrillo-Galvez, Fabián Flores-Bazán & Enrique López. (2020) A duality theory approach to the environmental/economic dispatch problem. Electric Power Systems Research 184, pages 106285.
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Refail Kasimbeyli, Zehra Kamisli Ozturk, Nergiz Kasimbeyli, Gulcin Dinc Yalcin & Banu Icmen Erdem. (2017) Comparison of Some Scalarization Methods in Multiobjective Optimization. Bulletin of the Malaysian Mathematical Sciences Society 42:5, pages 1875-1905.
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Shiva Kapoor & C. S. Lalitha. (2019) Stability and Scalarization for a Unified Vector Optimization Problem. Journal of Optimization Theory and Applications 182:3, pages 1050-1067.
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Fabián Flores-Bazán, Giandomenico Mastroeni & Cristián Vera. (2019) Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems. Journal of Optimization Theory and Applications 181:3, pages 787-816.
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Shiva Kapoor & C. S. Lalitha. (2019) Stability in unified semi-infinite vector optimization. Journal of Global Optimization 74:2, pages 383-399.
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Khushboo & C. S. Lalitha. (2019) A unified minimal solution in set optimization. Journal of Global Optimization 74:1, pages 195-211.
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María Alonso, Elvira Hernández & Elena Pereira. (2018) Optimality conditions and minimax properties in set optimization. Optimization Letters 13:1, pages 55-68.
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Ovidiu Bagdasar & Nicolae Popovici. (2018) Unifying local–global type properties in vector optimization. Journal of Global Optimization 72:2, pages 155-179.
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Khushboo & C. S. Lalitha. (2017) Scalarizations for a unified vector optimization problem based on order representing and order preserving properties. Journal of Global Optimization 70:4, pages 903-916.
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Michel H. Geoffroy, Yvesner Marcelin & Diana Nedelcheva. (2016) Convergence of relaxed minimizers in set optimization. Optimization Letters 11:8, pages 1677-1690.
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Hui Guo & Wan-li Zhang. (2016) Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems. Journal of the Operations Research Society of China 5:3, pages 419-430.
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Brian Dandurand & Margaret M. Wiecek. (2016) Quadratic scalarization for decomposed multiobjective optimization. OR Spectrum 38:4, pages 1071-1096.
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V. V. Gorokhovik & M. A. Trafimovich. (2016) First and second order optimality conditions in vector optimization problems with nontransitive preference relation. Proceedings of the Steklov Institute of Mathematics 292:S1, pages 91-105.
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César Gutiérrez, Vicente Novo, Juan Luis Ródenas-Pedregosa & Tamaki Tanaka. (2016) Nonconvex Separation Functional in Linear Spaces with Applications to Vector Equilibria. SIAM Journal on Optimization 26:4, pages 2677-2695.
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Hui Guo & Ke Quan Zhao. (2015) A kind of unified super efficiency via Assumption (A) and applications in vector optimization. Journal of Inequalities and Applications 2015:1.
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C. Gutiérrez, B. Jiménez & V. Novo. (2013) Optimality Conditions for Quasi-Solutions of Vector Optimization Problems. Journal of Optimization Theory and Applications 167:3, pages 796-820.
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Maurizio Chicco & Anna Rossi. (2015) Existence of Optimal Points Via Improvement Sets. Journal of Optimization Theory and Applications 167:2, pages 487-501.
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Nergiz Kasimbeyli. (2014) Existence and characterization theorems in nonconvex vector optimization. Journal of Global Optimization 62:1, pages 155-165.
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Ke-Quan Zhao, Yuan-Mei Xia & Xin-Min Yang. (2015) NONLINEAR SCALARIZATION CHARACTERIZATIONS OF $E$-EFFICIENCY IN VECTOR OPTIMIZATION. Taiwanese Journal of Mathematics 19:2.
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Ke Quan Zhao & Xin Min Yang. (2014) Characterizations of efficient and weakly efficient points in nonconvex vector optimization. Journal of Global Optimization 61:3, pages 575-590.
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Fabián Flores-Bazán, Fernando Flores-Bazán & Sigifredo Laengle. (2014) Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior. Journal of Optimization Theory and Applications 164:2, pages 455-478.
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Elvira Hernández. 2015. Set Optimization and Applications - The State of the Art. Set Optimization and Applications - The State of the Art 143 158 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 223 256 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 177 221 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 115 175 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 61 113 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 39 59 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 13 38 .
Sorin-Mihai GradSorin-Mihai Grad. 2015. Vector Optimization and Monotone Operators via Convex Duality. Vector Optimization and Monotone Operators via Convex Duality 1 11 .
Fang Lu & Chun-Rong Chen. (2014) Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications. Abstract and Applied Analysis 2014, pages 1-10.
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Ke Quan Zhao, Yuan Mei Xia & Hui Guo. (2014) A Characterization of -Benson Proper Efficiency via Nonlinear Scalarization in Vector Optimization . Journal of Applied Mathematics 2014, pages 1-5.
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Ke Quan Zhao & Yuan Mei Xia. (2014) A Kind of Unified Proper Efficiency in Vector Optimization. Abstract and Applied Analysis 2014, pages 1-5.
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Fabi?n Flores-Baz?n & Elvira Hern?ndez. (2011) Optimality conditions for a unified vector optimization problem with not necessarily preordering relations. Journal of Global Optimization 56:2, pages 299-315.
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