Some properties of sets, functions, and multi-objective optimization problems using p-convexity

TL;DR

This paper explores p-convexity in sets and functions, providing new algebraic and topological insights, and examines multi-objective optimization problems emphasizing weakly efficient minima under p-convexity assumptions.

Contribution

It introduces novel algebraic and topological results for p-convexity and analyzes solution sets in multi-objective optimization with p-convex component functions.

Findings

New algebraic properties of p-convex sets and functions

Characterizations of weakly efficient minima under p-convexity

Topological results related to p-convexity in Euclidean space

Abstract

In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze multi-objective optimization problems, with a particular emphasis on weakly efficient minima, under the assumption of $p$-convexity of the component functions. Several characterizations and properties of the corresponding solution sets are derived.