Topic 15 - Intro to KTT Conditions

We will call this g1 x x f x g 2 x recall the sets

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Unformatted text preview: aints. We will call this ̅. g1 (x) x f (x) g 2 (x) Recall the sets of improving and feasible directions, as defined in Topic #14. ̅ ̅ ̅ ̅ with ̅ for some ̅ for some ̅ ̅ and 175 ̅ } } Considering ̅ , graphically indicate the sets and . ̅ g1 (x) f (x) x g 2 (x) ̅ Note that ̅ a KKT point ̅ a KKT point for have the same set of gradients. ̅ solves ̅ , since the original problem and ̅ ̅ a solution to ̅ , ̅ ̅] Note the connection to Farkas’ Lemma: a solution to a solution to ̅ ( ) ̅ a solution to a solution ̅ ̅ “No improving feasible direction” ̅ ̅ “Can express ̅ as a non-negative linear combination of the gradients of the binding constraints” 176 Question: Are the K...
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This document was uploaded on 11/28/2013.

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