Multiobjective optimization with least constraint violation: optimality conditions and exact penalization

Jiawei Chen () and Yu-Hong Dai ()
Additional contact information
Jiawei Chen: Southwest University
Yu-Hong Dai: Chinese Academy of Sciences

Journal of Global Optimization, 2023, vol. 87, issue 2, No 21, 807-830

Abstract: Abstract Although multiobjective optimization problem (MOP) is useful for solving many practical optimization problems, it is possible that the constraints are inconsistent. In this paper, we reformulate MOP with possible inconsistent constraints into MOP with least constraint violation and provide necessary optimality conditions from the perspective of M-stationary point, Fritz-John stationary point and L-stationary point. A power penalty problem is proposed by using infeasibility measure of constraints. The calmness conditions of order $$\ell $$ ℓ of the MOP with least constraint violation and the local exact penalization of order $$\ell $$ ℓ of the power penalty problem are respectively introduced, which do not require the feasibility of the original MOP. We obtain the equivalence between the calmness of order $$\ell $$ ℓ of the MOP with least constraint violation and the local exact penalization of order $$\ell $$ ℓ of the power penalty problem. Necessary and sufficient conditions for calmness of order $$\ell $$ ℓ are also established under suitable conditions.

Keywords: Multiobjective optimization with least constraint violation; Optimality conditions; Exact penalization; Calmness; Infeasibility condition; 90C25; 90C46 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01158-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01158-8

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01158-8

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().