Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions

Shengjie Li (), Yangdong Xu (), Manxue You () and Shengkun Zhu ()
Additional contact information
Shengjie Li: Chongqing University
Yangdong Xu: Chongqing University of Posts and Telecommunications
Manxue You: Chongqing University
Shengkun Zhu: Southwestern University of Finance and Economics

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 3, 609-636

Abstract: Abstract Image space analysis is a new tool for studying scalar and vector constrained extremum problems as well as generalized systems. In the last decades, the introduction of image space analysis has shown that the image space associated with the given problem provides a natural environment for the Lagrange theory of multipliers and that separation arguments turn out to be a fundamental mathematical tool for explaining, developing and improving such a theory. This work, with its 3 parts, aims at contributing to describe the state-of-the-art of image space analysis for constrained optimization and to stress that it allows us to unify and generalize the several topics of optimization. In this 1st part, after a short introduction of such an analysis, necessary and sufficient optimality conditions are treated. Duality and penalization are the contents of the 2nd part. The 3rd part deals with generalized systems, in particular, variational inequalities and Ky Fan inequalities. Some further developments are discussed in all the parts.

Keywords: Image space analysis; Constrained extremum problem; Optimality condition; Regularity condition; 49K05; 90C29 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1247-z 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:joptap:v:177:y:2018:i:3:d:10.1007_s10957-018-1247-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1247-z

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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