English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we propose an Approximate Weak stationarity ($AW$-stationarity)concept designed to deal with {\em Mathematical Programs with CardinalityConstraints} (MPCaC), and we proved that it is a legitimate optimalitycondition independently of any constraint qualification. Such a sequentialoptimality condition improves weaker stationarity conditions, presented in aprevious work. Many research on sequential optimality conditions has beenaddressed for nonlinear constrained optimization in the last few years, someworks in the context of MPCC and, as far as we know, no sequential optimalitycondition has been proposed for MPCaC problems. We also establish somerelationships between our $AW$-stationarity and other usual sequentialoptimality conditions, such as AKKT, CAKKT and PAKKT. We point out that,despite the computational appeal of the sequential optimality conditions, inthis work we are not concerned with algorithmic consequences. Our aim is purelyto discuss theoretical aspects of such conditions for MPCaC problems.

A sequential optimality condition for Mathematical Programs with Cardinality Constraints