Book Chapter10.1007/978-3-642-54283-1_1
Variable Ordering Structures
Gabriele Eichfelder
- 01 Jan 2014
- pp 1-25
7
TL;DR: This chapter introduces variable ordering structures and examines their properties and focuses on special ordering maps where the images are Bishop-Phelps cones and discuss several applications.
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Abstract: In this chapter we recall basic concepts of partially ordered spaces and basic results on ordering cones and dual cones. We introduce variable ordering structures and examine their properties. We also focus on special ordering maps where the images are Bishop-Phelps cones and discuss several applications.
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Citations
Fixed Points and Variational Principles with Applications to Capability Theory of Wellbeing via Variational Rationality
TL;DR: In this paper, a variational analysis for parametric dynamic systems in quasimetric spaces is presented, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces.
41
Scalarization andpointwise well-posedness for set optimization problems
Xian-Jun Long,Jian-Wen Peng,Zai-Yun Peng +2 more
- 01 Jan 2015
TL;DR: In this paper, the equivalence relations between three kinds of pointwise well-posedness for set optimization problems and three different kinds of scalar optimization problems were established. But the equivalences between the three kinds were not defined.
30
Outlook and Further Application Areas
Gabriele Eichfelder
- 01 Jan 2014
TL;DR: The theory of consumer demand in economics is also related to variable ordering structures in vector variational inequalities, vector complementarity and equilibrium problems and an application in the treatment planning in intensity-modulated radiation therapy is discussed.
1
Scalarizations for Variable Orderings Given by Bishop-Phelps Cones
Gabriele Eichfelder
- 01 Jan 2014
TL;DR: In this paper, variable ordering structures are defined by ordering maps with images being Bishop-Phelps (BP) cones and a new scalarization functional which is also new in partially ordered spaces is introduced.
1
Cone-Valued Maps
Gabriele Eichfelder
- 01 Jan 2014
TL;DR: In this paper, cone-valued maps are defined by ordering maps which are conevalued maps, and variable ordering structures are defined using ordering maps that are cone valued maps, such as cone-convexity, linearity or monotonicity.
1
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Minimax Theorems
TL;DR: Come with us to read a new book that is coming recently, this is a new coming book that many people really want to read will you be one of them?
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Theory of Multiobjective Optimization
Yoshikazu Sawaragi,Tetsuzo Tanino,Hirotaka Nakayama +2 more
- 12 Oct 1985
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