On the exactness and the convergence of the $$l_{1}$$ l 1 exact penalty E-function method for E-differentiable optimization problems

Tadeusz Antczak () and Najeeb Abdulaleem ()
Additional contact information
Tadeusz Antczak: University of Łódź
Najeeb Abdulaleem: University of Łódź

OPSEARCH, 2023, vol. 60, issue 3, No 12, 1359 pages

Abstract: Abstract This paper is devoted to introduce and investigate a new exact penalty function method which is called the $$l_{1}$$ l 1 exact penalty E-function method. Namely, we use the aforesaid exact penalty function method to solve a completely new class of nonconvex (not necessarily) differentiable mathematical programming problems, that is, E-differentiable minimization problems. Then, we analyze the most important from a practical point of view property of all exact penalty function methods, that is, exactness of the penalization. Thus, under appropriate E-convexity hypotheses, we prove the equivalence between the original E-differentiable extremum problem and its corresponding penalized optimization problem created in the introduced $$l_{1}$$ l 1 exact penalty E-function method. Further, we also present and investigate the algorithm for this exact penalty function method which minimizes the $$l_{1}$$ l 1 exact penalty E-function. The convergence theorem for the aforesaid algorithm is also established.

Keywords: E-differentiable optimization problem; $$l_{1}$$ l 1 exact; Penalized E-optimization problem; Exactness of the penalization; E-Karush–Kuhn–Tucker necessary optimality conditions; E-convex function; 49M30; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12597-023-00663-y 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:opsear:v:60:y:2023:i:3:d:10.1007_s12597-023-00663-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/12597

DOI: 10.1007/s12597-023-00663-y

Access Statistics for this article

OPSEARCH is currently edited by Birendra Mandal

More articles in OPSEARCH from Springer, Operational Research Society of India
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().