with?+?±?(x)=0and?−?±?(x0²=1,2,...,³DeFning??=?+?−?−?, (5.100) can be written as´µ(x∗∑??´±?[x∗]which is the Frst-order condition for an equality constrained problem. ±urthermore, ifx∗satisFes the inequality constraints±(x∗)≤0and±(x∗)≥0it satisFes the equality±(x∗05.34Suppose thatx∗solves the problemmaxxc±xsubject to¶x≤0with Lagrangean·=c±x−?±¶xThen there exists?≥0 such that´x·=c±−?±¶=0that is,¶±?=c. Conversely, if there is no solution, there existsxsuch that¶x≤0andc±x>c±0=05.35There are two binding constraints at (4,0), namely±(¸1,¸2¸1+¸2≤4ℎ(¸12−¸2≤0with gradients∇±(4,0) = (1,1)∇ℎ(4,0) = (0,1)which are linearly independent. Therefore the binding constraints are regular at (0
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