Nonnegative Weighted sums

Finite sums

  • , is convex
  • is convex

Infinite sums

略

Composition with an affine mapping

  • Affine mappings

    holds convexity

Pointwise Maximum

is convex

is convex

Proof is simple.

Compositions

  • h,g are convex
  • is convex in some conditions <!–TODO: finish convex conditions>