Nonconvex vector optimization of set-valued mappings☆
By Shengjie Li, Xiaoqi Yang, Guangya Chen. 2003
50 citations recorded by the source corpus.
In this paper, we discuss properties, such as monotonicity and continuity, of the Gerstewitz's nonconvex separation functional. With the aid of this functional, necessary and sufficient optimality conditions for nonconvex optimization problems of set-valued mappings are obtained in topological vector spaces.
Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ae02a1838acdd498625946b6e349e80a31113a7b
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In Civil and Structural Engineering
In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Nonconvex scalarization in set optimization with set-valued maps (2007, methodology): “This function has many properties of separation (see [6,14,15]) and plays an important role in many areas, for instance, in the vector equilibrium problem [4,17].”
- Higher-Order Optimality Conditions for Set-Valued Optimization (2008, unknown): “Now we give the following proposition for explaining that (13) holds when F or G is locally Lipschitz.”
- Lagrangian Duality in Set-Valued Optimization (2007, unknown): “[2–8].”