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First and second order sufficient conditions for strict minimality in nonsmooth vector optimization

✍ Scribed by Bienvenido Jiménez; Vicente Novo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
150 KB
Volume
284
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function. With this aim, the notion of support function to a vector problem is introduced, in such a way that the scalar case and the multiobjective case, in particular, are contained. The obtained results extend the multiobjective ones to this case. Moreover, specializing to a feasible set defined by equality, inequality, and set constraints, first and second order sufficient conditions by means of Lagrange multiplier rules are established.

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## Abstract It has been common practice to find controls satisfying only necessary conditions for optimality, and then to use these controls assuming that they are (locally) optimal. However, sufficient conditions need to be used to ascertain that the control rule is optimal. Second order sufficien