Local maximum points of explicitly quasiconvex functions

This work concerns generalized convex real-valued functions defined on a nonempty convex subset of a real topological linear space. Its aim is twofold: first, to show that any local maximum point of an explicitly quasiconvex function is a global minimum point whenever it belongs to the intrinsic core of the function’s domain and second, to characterize strictly convex normed spaces by applying this property for a particular class of convex functions

Inflationary differential evolution for Constrained Multi-Objective Optimisation Problem

In this paper we review several parameter-based scalarisation approaches used within Multi-Objective Optimisation. We propose then a proof-of-concept for a new memetic algorithm designed to solve the Constrained Multi-Objective Optimisation Problem. The algorithm is finally tested on a benchmark with a series of difficulties

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Unifying local-global type properties in vector optimization.

It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min - global min” and “local max - global min” type properties can be extended and unified by a single general localglobal extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local-global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.Nicolae Popovici’s research was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE- 2016-0190, within PNCDI III