Convex conjugate

For two functions $f_0$ and $f_1$ and a number $0\le \lambda\le 1$ the convexity relation

holds. The $\star$ operation is a convex mapping itself.

The infimal convolution (or epi-sum) of two functions f and g is defined as

Let f₁, …, f_m be proper, convex and lsc functions on R. Then the infimal convolution is convex and lsc (but not necessarily proper), and satisfies

单词	Infimal convolution
释义	Infimal convolution 英语百科 Convex conjugate Convexity For two functions $f_0$ and $f_1$ and a number $0\le \lambda\le 1$ the convexity relation holds. The $\star$ operation is a convex mapping itself. The infimal convolution (or epi-sum) of two functions f and g is defined as Let f₁, …, f_m be proper, convex and lsc functions on R. Then the infimal convolution is convex and lsc (but not necessarily proper), and satisfies
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Infimal convolution