10-hw116 - MATHEMATICS 116, FALL 2007 CONVEXITY AND...

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MATHEMATICS 116, FALL 2007 CONVEXITY AND OPTIMIZATION WITH APPLICATIONS Assignment #10 Last modified: December 3, 2007 Due Thursday, December 6 at class. All these problems are relevant to the quiz on that date. 1. Luenberger, Problem 7.14.1. This is an interesting question, but I am not convinced that I have found any x ( t ) for which the Gateaux differential is linear. To start, consider the linearity requirement, difficult to meet, that δf ( x ; h ) + δf ( x ; - h ) = 0 . 2. Luenberger, Problem 7.14.4. 3. Solve the campaign chest problem done in class for the case where, in addition to interest on your balance, you get contributions at a unit rate from a PAC, so that the amount the you need to contribute is only ˙ x ( t ) - x ( t ) - 1. 4. Your local trash collectors have the motto, “Them that has, gets it taken away,” and so if the pile of trash outside your room has size x ( t ), it gets taken away continuously in such a way that ˙ x ( t ) = - x ( t ). This is not good enough for you, since
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10-hw116 - MATHEMATICS 116, FALL 2007 CONVEXITY AND...

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