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Jiménez, Bienvenido; Novo, Vicente

First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. (English) Zbl 1033.90120

J. Math. Anal. Appl. 284, No. 2, 496-510 (2003).
Summary: 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.

Cited in 1 Review
Cited in 43 Documents

MSC:

90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming

Keywords:

Vector optimization; Strict local minimum; First and second order sufficient optimality conditions; Support function
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\textit{B. Jiménez} and \textit{V. Novo}, J. Math. Anal. Appl. 284, No. 2, 496--510 (2003; Zbl 1033.90120)
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References:

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