Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints

YC Liang, XD Zhu, GH Lin - Set-Valued and Variational Analysis, 2014 - Springer
YC Liang, XD Zhu, GH Lin
Set-Valued and Variational Analysis, 2014Springer
This paper considers the mathematical program with second-order cone complementarity
constrains (MPSOCC). As a generalization of the developed mathematical program with
complementarity constrains (MPCC), MPSOCC has many applications in practice. Motivated
by the MPCC theory, several stationarity concepts, which include the Clarke-type,
Mordukhovich-type, and strong stationarities, are presented in this paper. It is further shown
that a local minimizer of MPSOCC must be stationary in some sense under suitable …
Abstract
This paper considers the mathematical program with second-order cone complementarity constrains (MPSOCC). As a generalization of the developed mathematical program with complementarity constrains (MPCC), MPSOCC has many applications in practice. Motivated by the MPCC theory, several stationarity concepts, which include the Clarke-type, Mordukhovich-type, and strong stationarities, are presented in this paper. It is further shown that a local minimizer of MPSOCC must be stationary in some sense under suitable conditions. This indicates that these stationarity concepts are reasonable in theory.
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