TY - JOUR
T1 - Criticality of Lagrange multipliers in extended nonlinear optimization
AU - Do, Hong
AU - Mordukhovich, Boris S.
AU - Sarabi, M. Ebrahim
N1 - Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - The paper is devoted to the study and applications of criticality of Lagrange multipliers in variational systems, which are associated with the class of problems in composite optimization known as extended nonlinear programming (ENLP). The importance of both ENLP and the concept of multiplier criticality in variational systems has been recognized in theoretical and numerical aspects of optimization and variational analysis, while the criticality notion has never been investigated in the ENLP framework. We present here a systematic study of critical and noncritical multipliers in a general variational setting that covers, in particular, KKT systems in ENLP with establishing their verifiable characterizations as well as relationships between noncriticality and other stability notions in variational analysis. Our approach is mainly based on advanced tools of second-order variational analysis and generalized differentiation.
AB - The paper is devoted to the study and applications of criticality of Lagrange multipliers in variational systems, which are associated with the class of problems in composite optimization known as extended nonlinear programming (ENLP). The importance of both ENLP and the concept of multiplier criticality in variational systems has been recognized in theoretical and numerical aspects of optimization and variational analysis, while the criticality notion has never been investigated in the ENLP framework. We present here a systematic study of critical and noncritical multipliers in a general variational setting that covers, in particular, KKT systems in ENLP with establishing their verifiable characterizations as well as relationships between noncriticality and other stability notions in variational analysis. Our approach is mainly based on advanced tools of second-order variational analysis and generalized differentiation.
KW - 49J52
KW - 49J53
KW - 90C31
KW - Variational analysis
KW - composite optimization
KW - critical and noncritical multipliers
KW - extended nonlinear programming
KW - generalized differentiation
KW - stability of variational systems
UR - http://www.scopus.com/inward/record.url?scp=85079062780&partnerID=8YFLogxK
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U2 - 10.1080/02331934.2020.1723585
DO - 10.1080/02331934.2020.1723585
M3 - Article
AN - SCOPUS:85079062780
SN - 0233-1934
VL - 70
SP - 511
EP - 544
JO - Optimization
JF - Optimization
IS - 3
ER -