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lagrange multiplier rule

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Generalized Lagrange multiplier rule for non-convex vector optimization problems
Part of
- Miscellaneous applications of functional analysis
Maria Bernadette Donato
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 2 / April 2016

Published online by Cambridge University Press:

03 March 2016, pp. 297-308

Print publication:

April 2016
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In this paper a non-convex vector optimization problem among infinite-dimensional spaces is presented. In particular, a generalized Lagrange multiplier rule is formulated as a necessary and sufficient optimality condition for weakly minimal solutions of a constrained vector optimization problem, without requiring that the ordering cone that defines the inequality constraints has non-empty interior. This paper extends the result of Donato (J. Funct. Analysis261 (2011), 2083–2093) to the general setting of vector optimization by introducing a constraint qualification assumption that involves the Fréchet differentiability of the maps and the tangent cone to the image set. Moreover, the constraint qualification is a necessary and sufficient condition for the Lagrange multiplier rule to hold.