781 research outputs found
Lp-norms, Log-barriers and Cramer transform in Optimization
We show that the Laplace approximation of a supremum by Lp-norms has
interesting consequences in optimization. For instance, the logarithmic barrier
functions (LBF) of a primal convex problem P and its dual appear naturally when
using this simple approximation technique for the value function g of P or its
Legendre-Fenchel conjugate. In addition, minimizing the LBF of the dual is just
evaluating the Cramer transform of the Laplace approximation of g. Finally,
this technique permits to sometimes define an explicit dual problem in cases
when the Legendre-Fenchel conjugate of g cannot be derived explicitly from its
definition
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