# Efficient Solutions in Generalized Linear Vector Optimization

## TL;DR

This paper advances the understanding of generalized linear vector optimization by establishing new properties of convex sets, deriving a scalarization formula, and characterizing the structure of efficient solution sets in topological vector spaces.

## Contribution

It introduces new results on generalized polyhedral convex sets and provides a scalarization formula for efficient solutions in generalized vector optimization.

## Key findings

- Efficient solution sets are unions of finitely many generalized polyhedral convex sets.
- Efficient solution sets are connected by line segments.
- New properties of generalized polyhedral convex sets are established.

## Abstract

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector optimization problems is obtained. We also prove that the efficient solution set of a generalized linear vector optimization problem in a locally convex Hausdorff topological vector space is the union of finitely many generalized polyhedral convex sets and it is connected by line segments.