A perturbational duality approach in vector optimization

Abstract

A perturbational vector duality approach for objective functions $f:X\to {\bar{L}}^0$ is developed, where $X$ is a Banach space and ${\bar{L}}^0$ is the space of extended real valued functions on a measure space, which extends the perturbational approach from the scalar case. The corresponding strong duality statement is proved under a closedness type regularity condition. Optimality conditions and a Moreau-Rockafellar type formula are provided. The results are specialized for constrained and unconstrained problems. Examples of integral operators and risk measures are discussed.

arXiv comment14 pages

References in corpus (2)

• The algebra of conditional sets and the concepts of conditional topology and compactness
• On compactness in $L^0$-modules

Cited by in corpus (1)

• A Fenchel-Moreau theorem for ${\bar{L}}^0$-valued functions