: Convex Analysis and Optimization Homework 1

| i ∈ I} of cones is a cone. (c) Show that the image and the inverse image of a cone under a linear transformation is a cone. (d) Show that the vector sum C. 1 + C. 2. of two cones C. 1. and C. 2. is a cone. (e) Show that a subset C is a convex cone if and only if it is closed under addition and positive

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Show that is linearfractional, and that the matrix associated with it is the product E f gT h A b cT d : Dual of exponential cone. The exponential cone K exp R3 is de ned as K exp = f(x;y;z) jy>0; yex=y zg: Find the dual cone K exp. We are not worried here about the ne details of what happens on the boundaries of these cones, so you really needn't worry about it. But we make some ...

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