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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

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Convexity of a positive definite objective with min(x,y)-nonlinearity

I have derived an optimization objective of the form $$ f(x) = \sum_{i,j} C_{ij}\min(x_i, x_j), s.t. g(x) \geq 0 $$ where $C \in \mathcal{R}^{N \times N}$ is a positive definite matrix, and $x \in \ma …
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