mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also...

function. Both LogSumExp and softmax are used in machine learning. The convex conjugate (specifically, the Legendre transform) of the softplus function is...

version for conjugate Hölder exponents. For details and generalizations we refer to the paper of Mitroi & Niculescu. By denoting the convex conjugate of a real...

dp^{2}}\operatorname {H} _{\text{b}}(p)=-{\frac {1}{p(1-p)\ln 2}}} The convex conjugate (specifically, the Legendre transform) of the binary entropy (with...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

The convex conjugate of an extended real-valued function f : X → [ − ∞ , ∞ ] {\displaystyle f:X\to [-\infty ,\infty ]} (not necessarily convex) is the...

which identifies equivalent dynamical systems Convex conjugate, the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation...

nonnegative matrix is a convex function of its diagonal elements. Concave function Convex analysis Convex conjugate Convex curve Convex optimization Geodesic...

spaces Convex function, when the line segment between any two points on the graph of the function lies above or on the graph Convex conjugate, of a function...

which means the gradient of LogSumExp is the softmax function. The convex conjugate of LogSumExp is the negative entropy. The LSE function is often encountered...