Figure A4.

Minimization of $\widehat{M}$ Should the constraints ĉ_i(x) ≥ 0 be inconsistent with one another within the trust region ∥x − x₀∥₂ ≤ _ρ, the candidate vertex x* is chosen to minimize $\widehat{M}≔\text{max}\left\{-{\widehat{c}}_i(x):i=1,\dots ,m\right\}$. (top) The constraints ĉ₁(x) ≥ 0 and ĉ₂(x) ≥ 0 are inconsistent within the region ∥x − x₀∥₂ ≤ ρ. (bottom left) Graphs of the affine functions −ĉ₁(x) (blue) and −ĉ₂(x) (green). (bottom right) The vertex x* is defined to be the point within the trust region (black circle) at which $\widehat{M}$ is minimized.