Fig. 2.

Contours show RED cost C_red(x_{α, β}) from (14) and arrows show RED-algorithm gradient field g(x_{α, β}) from (46) versus (α, β), where ${\mathit{x}}_{\alpha ,\beta }=\widehat{\mathit{x}}+\alpha {\mathit{e}}_1+\beta {\mathit{e}}_2$ with randomly chosen e₁ and e₂. The subplots show that the minimizer of C_red(x_{α, β}) is not the fixed-point $\widehat{\mathit{x}}$, and that C_red(·) may be non-smooth and/or non-convex.