## Details

Original language | English |
---|---|

Journal | OPTIMIZATION |

Publication status | E-pub ahead of print - Aug 2024 |

## Abstract

We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.

## Keywords

- Generalized convexity, nonlinear scalarization function, vector function

## ASJC Scopus subject areas

- Mathematics(all)
**Control and Optimization**- Mathematics(all)
**Applied Mathematics**- Decision Sciences(all)
**Management Science and Operations Research**

## Cite this

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**A new concept of semistrict quasiconvexity for vector functions.**/ Günther, Christian; Orzan, Alexandru; Popovici, Nicolae.

In: OPTIMIZATION, 08.2024.

Research output: Contribution to journal › Article › Research › peer review

*OPTIMIZATION*. https://doi.org/10.1080/02331934.2024.2384919

*OPTIMIZATION*. Advance online publication. https://doi.org/10.1080/02331934.2024.2384919

}

TY - JOUR

T1 - A new concept of semistrict quasiconvexity for vector functions

AU - Günther, Christian

AU - Orzan, Alexandru

AU - Popovici, Nicolae

N1 - Publisher Copyright: © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

PY - 2024/8

Y1 - 2024/8

N2 - We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.

AB - We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.

KW - Generalized convexity

KW - nonlinear scalarization function

KW - vector function

UR - http://www.scopus.com/inward/record.url?scp=85200266301&partnerID=8YFLogxK

U2 - 10.1080/02331934.2024.2384919

DO - 10.1080/02331934.2024.2384919

M3 - Article

JO - OPTIMIZATION

JF - OPTIMIZATION

SN - 0323-3898

ER -