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For questions involving the concept of convexity
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How to find the necessary and sufficient conditions for a non-convex function to be locally ...
See for example Chapter 3 of "Convex Optimization", Boyd for operations that preserve convexity. … for global convexity, thus local and global convexity are the same concept.
3) There are criteria for determining if a matrix is positive definite that do not involve the characteristic polynomila, namely …