期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 337, 期 1, 页码 292-310出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2007.03.087
关键词
mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; optimality conditions; constraint qualifications; limiting normal cone
We consider a class of optimization problems that is called a mathematical program with vanishing constraints (MPVC for short). This class has some similarities to mathematical programs with equilibrium constraints (MPECs for short), and typically violates standard constraint qualifications, hence the well-known Karush-Kuhn-Tucker conditions do not provide necessary optimality criteria. In order to obtain reasonable first order conditions under very weak assumptions, we introduce several MPVC-tailored constraint qualifications, discuss their relation, and prove an optimality condition which may be viewed as the counterpart of what is called M-stationarity in the MPEC-field. (C) 2007 Elsevier Inc. All rights reserved.
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