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- W2016066906 abstract "We consider the vector optimization problem min C f ( x ) , g ( x ) ∈ − K , where f : R n → R m and g : R n → R p are C 0 , 1 (i.e. locally Lipschitz) functions and C ⊆ R m and K ⊆ R p are closed convex cones. We give several notions of solution (efficiency concepts), among them the notion of properly efficient point ( p -minimizer) of order k and the notion of isolated minimizer of order k . We show that each isolated minimizer of order k ⩾ 1 is a p -minimizer of order k . The possible reversal of this statement in the case k = 1 is studied through first order necessary and sufficient conditions in terms of Dini derivatives. Observing that the optimality conditions for the constrained problem coincide with those for a suitable unconstrained problem, we introduce sense I solutions (those of the initial constrained problem) and sense II solutions (those of the unconstrained problem). Further, we obtain relations between sense I and sense II isolated minimizers and p -minimizers." @default.
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- W2016066906 date "2005-09-01" @default.
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- W2016066906 title "Isolated minimizers and proper efficiency for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> constrained vector optimization problems" @default.
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- W2016066906 doi "https://doi.org/10.1016/j.jmaa.2005.01.041" @default.
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