Dual Representation of Quasiconvex Conditional Maps
Marco Frittelli, Marco Maggis
TL;DR
This paper introduces a dual representation for quasiconvex maps between lattices of random variables, extending existing duality results for real-valued functions and convex maps to a more general setting.
Contribution
It generalizes the dual representation theory to quasiconvex maps between lattices of random variables, broadening the scope of duality in mathematical analysis.
Findings
Provides a dual representation in terms of conditional expectations.
Generalizes duality results from real-valued functions to lattice-valued maps.
Extends the dual representation framework to quasiconvex maps.
Abstract
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.
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Taxonomy
TopicsMulti-Criteria Decision Making · Optimization and Variational Analysis · Fuzzy Systems and Optimization