The geometric vector inequality and its properties

Abstract

The present paper contains properties of the geometric vector inequality, introduced in [4] and [12]. Such properties are of interest not only in itself, but they are also useful for a systematic treatment of special structured vector optimization problems, denoted as geometric vector optimization problems. Especially, a close connection to the Fenchel vector conjugate as well as to the Legendre vector transform will be shown

Keywords:

• Vector Optimization
• Geometric Vector Inequality
• Geometric Programming
• Fenchel Vector Conjugate
• Legendre Vector Transform