Vector optimization - theory, applications, and extensions

By J. Jahn. 2004

900 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5d24fd34afd70c702d04e794017273d88fe0a949

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Citations in the corpus

A survey of recent developments in multiobjective optimization (2007, background): “For a comprehensive review of theory and applications of multiobjective programming, the reader is referred to Hillermeier (2001), Jahn (2004) , Pardalos et al. (1995), Steuer (1986) and Miettinen (1999).”
A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization (2018, background): “Optimization problems with set-valued data arose originally inside of the theory of vector optimization and have recently been attracted more attention due to their important real-world applications in socio-economics, see [1,2], and a survey given in [3].”
Solution concepts in vector optimization: a fresh look at an old story (2011, background): “Introduction The theory of vector optimization [11,19,23] has a number of structural differences in contrast to scalar optimization.”
Higher-Order Optimality Conditions for Set-Valued Optimization (2008, unknown): “T [(2) Graph(F−S,G−D)(x0, y0, z0, u1, v1, w1) = {(x, (y, z)) ∈ R×R 2 | y ≤ 0, z ≤ 2x},”
Fuzzy necessary optimality conditions for vector optimization problems (2009, background): “K which for all z, z1, z22Z and for all 2R satisfies: 1: jjjzjjj ¼ 0()z ¼ 0; 2: jjj z jjj ¼ j j jjjzjjj; 3: jjjz1 þ z2jjj 2 jjjz1jjj þ jjjz2jjj K: A subdifferential (denoted @ ) for vector-valued functions was proposed by Jahn in [22] and for the particular case of above vector-valued norm jjj jjj i”
An Abstract Framework for Elliptic Inverse Problems: Part 2. An Augmented Lagrangian Approach (2009, background): “1 Then a well-known separation theorem (see [26]) ensures the existence of functionals p1 p2 V not both zero, such that for all a A V s 0 t we have”
Lagrangian Duality in Set-Valued Optimization (2007, background): “[15], the set optimization criterion opens a wide and promising field of research.”
Vilfredo Pareto and multi-objective optimization (2012, background): “…(Chankong and Haimes, 1983, p. 113); “Edgeworth and Pareto were probably Documenta Mathematica · Extra Volume ISMP (2012) 447–453 the first who introduced an optimality concept for such problems” (Jahn, 2004, p. 113); “wurden besonders von F.Y. Edgeworth (1845–1926) and V. Pareto (1848–1929 [sic”
Set-valued optimization in welfare economics (2010, background): “They correspond to similar Paretotype concepts (weakly efficient and efficient solutions) for standard problems of vector optimization in the case of preferences given by utility functions; see, e.g., [ 14 , 20, 22] and the references therein.”
Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces (2010, background): “For example, the reader can look at the monographs of Luc [2], Gopfert, Riahi, Tammer and Zu [3] and Jahn [ 4 ].”