Details
| Original language | English |
|---|---|
| Pages (from-to) | 651-686 |
| Number of pages | 36 |
| Journal | Journal of Nonlinear and Variational Analysis |
| Volume | 7 |
| Issue number | 5 |
| Publication status | Published - 1 Oct 2023 |
Abstract
The aim of this paper is to present a vectorial penalisation approach for vector optimisation problems in which the vector-valued objective function acts between real linear-topological spaces X and Y, where the image space Y is partially ordered by a pointed convex cone. In essence, the approach replaces the original constrained vector optimisation problem (with not necessarily convex feasible set) by two unconstrained vector optimisation problems, where in one of the two problems a penalisation term (function) with respect to the original feasible set is added to the vector objective function. To derive our main results, we use a generalised convexity (quasiconvexity) notion for vector functions in the sense of Jahn. Our results extend/generalise known results in the context of vectorial penalisation in multiobjective/vector optimisation. We put a special emphasis on the construction of appropriate penalisation functions for several popular classes of (vector) optimisation problems (e.g., semidefinite/copositive programming, second-order cone programming, optimisation in function spaces).
Keywords
- Generalised Convexity, Pareto Efficiency, Penalisation, Vector Optimisation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of Nonlinear and Variational Analysis, Vol. 7, No. 5, 01.10.2023, p. 651-686.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Vectorial Penalisation in Vector Optimisation in Real Linear-Topological Spaces
AU - Günther, Christian
AU - Köbis, Elisabeth
AU - Schmölling, Paul
AU - Tammer, Christiane
PY - 2023/10/1
Y1 - 2023/10/1
N2 - The aim of this paper is to present a vectorial penalisation approach for vector optimisation problems in which the vector-valued objective function acts between real linear-topological spaces X and Y, where the image space Y is partially ordered by a pointed convex cone. In essence, the approach replaces the original constrained vector optimisation problem (with not necessarily convex feasible set) by two unconstrained vector optimisation problems, where in one of the two problems a penalisation term (function) with respect to the original feasible set is added to the vector objective function. To derive our main results, we use a generalised convexity (quasiconvexity) notion for vector functions in the sense of Jahn. Our results extend/generalise known results in the context of vectorial penalisation in multiobjective/vector optimisation. We put a special emphasis on the construction of appropriate penalisation functions for several popular classes of (vector) optimisation problems (e.g., semidefinite/copositive programming, second-order cone programming, optimisation in function spaces).
AB - The aim of this paper is to present a vectorial penalisation approach for vector optimisation problems in which the vector-valued objective function acts between real linear-topological spaces X and Y, where the image space Y is partially ordered by a pointed convex cone. In essence, the approach replaces the original constrained vector optimisation problem (with not necessarily convex feasible set) by two unconstrained vector optimisation problems, where in one of the two problems a penalisation term (function) with respect to the original feasible set is added to the vector objective function. To derive our main results, we use a generalised convexity (quasiconvexity) notion for vector functions in the sense of Jahn. Our results extend/generalise known results in the context of vectorial penalisation in multiobjective/vector optimisation. We put a special emphasis on the construction of appropriate penalisation functions for several popular classes of (vector) optimisation problems (e.g., semidefinite/copositive programming, second-order cone programming, optimisation in function spaces).
KW - Generalised Convexity
KW - Pareto Efficiency
KW - Penalisation
KW - Vector Optimisation
UR - http://www.scopus.com/inward/record.url?scp=85174252707&partnerID=8YFLogxK
U2 - 10.23952/jnva.7.2023.5.02
DO - 10.23952/jnva.7.2023.5.02
M3 - Article
AN - SCOPUS:85174252707
VL - 7
SP - 651
EP - 686
JO - Journal of Nonlinear and Variational Analysis
JF - Journal of Nonlinear and Variational Analysis
SN - 2560-6921
IS - 5
ER -