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Results tagged with convex-optimization
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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
7
votes
Why are $\Gamma_0$ functions called this
It seems the notation $\Gamma_0$ was introduced by Jean-Jacques Moreau in Proximité et dualité dans un espace Hilbertien (1965), as a generalisation of the notion of projection onto a convex domain (s …
- 188k
4
votes
Least square solution to $AXB+CXD=E$
This is the Sylvester equation. A simple explicit solution is possible under certain conditions (no common eigenvalues of the matrices $C^{-1}A$ and $-DB^{-1}$), as explained in the Wikipedia page. Th …
- 188k
4
votes
About optimization with Renyi divergence
For the requested examples see Rényi Divergence and Kullback-Leibler Divergence (2012).
• Two continuous distributions: Equation 10 gives the Rényi divergence between two Gaussian distributions (mean …
- 188k
4
votes
Gradient descent relaxation dynamics of a Euler-Lagrange equation
The usual way to ensure the convergence of the steepest descent formulation of the Euler-Lagrange equations, is to introduce a friction term, see The Calculus of Variations by Jeff Calder. Instead of
…
- 188k
3
votes
Abstract treatment of multivariate calculus relevant for optimization
You might appreciate: Multivariate Statistics: A Vector Space Approach, Morris Eaton, described here:
My interest in the coordinate-free approach to linear statistical problems was motivated by at …
- 188k
1
vote
Minimize the variance of a Boltzmann distribution
A way to approach your problem could be to consider the calculation of the expectation value as a Monte Carlo integration. Then you can use established techniques of variance reduction, as described f …
- 188k