Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/27423
Title: Lagrange multipliers and calmness conditions of order p
Authors: Yang, XQ 
Meng, ZQ
Keywords: Dini directional derivative
Generalized calmness condition
Lagrange multiplier
non-Lipschitz penalty function
Issue Date: 2007
Publisher: Institute for Operations Research and the Management Sciences
Source: Mathematics of operations research, 2007, v. 32, no. 1, p. 95-101 How to cite?
Journal: Mathematics of operations research 
Abstract: In this paper, by assuming that a non-Lipschitz penalty function is exact, new conditions for the existence of Lagrange multipliers are established for an inequality and equality-constrained continuously differentiable optimization problem. This is done by virtue of a first-order necessary optimality condition of the penalty problem, which is obtained by estimating Dini upper-directional derivatives of the penalty function in terms of Taylor expansions, and a Farkas lemma. Relations among the obtained results and some well-known constraint qualifications are discussed.
URI: http://hdl.handle.net/10397/27423
ISSN: 0364-765X
EISSN: 1526-5471
DOI: 10.1287/moor.1060.0217
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