A perturbational duality approach in vector optimization

Asgar Jamneshan; Sorin-Mihai Grad

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arXiv · 1807.02666

A perturbational duality approach in vector optimization

Asgar Jamneshan·Sorin-Mihai Grad

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Abstract

A perturbational vector duality approach for objective functions $f\colon X\to \bar{L}^0$ 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.

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Asgar Jamneshan, Sorin-Mihai Grad. 2018-07-07. A perturbational duality approach in vector optimization. https://arxiv.org/abs/1807.02666

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