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.
Original language | English |
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Pages (from-to) | 95-101 |
Number of pages | 7 |
Journal | Mathematics of Operations Research |
Volume | 32 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2007 |
Keywords
- Dini directional derivative
- Generalized calmness condition
- Lagrange multiplier
- non-Lipschitz penalty function
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Management Science and Operations Research