Preprint Article Version 1 This version is not peer-reviewed

# Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity

Version 1 : Received: 6 March 2020 / Approved: 7 March 2020 / Online: 7 March 2020 (08:52:27 CET)

How to cite: Jennane, M.; El Fadil, L.; Kalmoun, E.M. Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity. Preprints 2020, 2020030118 (doi: 10.20944/preprints202003.0118.v1). Jennane, M.; El Fadil, L.; Kalmoun, E.M. Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity. Preprints 2020, 2020030118 (doi: 10.20944/preprints202003.0118.v1).

## Abstract

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

## Subject Areas

interval-valued vector optimization problems; generalized approximate LU-convexity; interval vector variational inequalities; LU-efficient solutions

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