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The conventional Lagrangian approach to solving constrained optimization problems leads to optimality conditions which are either necessary, or sufficient, but not both unless the underlying cost and constraint functions are also convex. We introduce a new approach based on the Tchebyshev norm. This leads to an optimality condition which is both sufficient and necessary, without any convexity assumption...
In information theory, the fundamental tool is the entropy function, whose upper bound is derived by the use of Jensen Inequality. In this paper, we extend the Jensen Inequality and apply it to derive some useful lower bounds for various entropy measures of discrete random variables.
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