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\begin{aligned} Δ z_{c} + Δ v_{c} & = 0 \\ A Δ z_{c} & = 0 \\ A^{'} Δ t_{c} + Δ s_{c} - Δ w_{c} & = 0 \\ S Δ z_{c} + Z Δ s_{c} & = - Z_{a f f} S_{a f f} e + σ μ e \\ V Δ w_{c} + W Δ v_{c} & = - V_{a f f} W_{a f f} e + σ μ e \\ where ζ_{s t a r t} = z^{'} s + v^{'} w, & complementarity at the start of the iteration \\ ζ_{a f f} = z_{a f f}^{'} s_{a f f} + v_{a f f}^{'} w_{a f f}, & the affine complementarity \\ μ = ζ_{a f f} / 2 n, & the average complementarity \\ σ = (ζ_{a f f} / ζ_{s t a r t})^{3} \end{aligned}

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Math as LaTeX Source

\begin{align*} \bDelta z_ c + \bDelta v_ c & = \mb{0} \\ \bA \bDelta z_ c & = \mb{0}\\ \bA ^{\prime } \bDelta t_ c + \bDelta s_ c - \bDelta w_ c & = \mb{0}\\ \bS \bDelta z_ c + \bZ \bDelta s_ c & = - \bZ _{\mathit{aff}} \bS _{\mathit{aff}} \mb{e} + \sigma \bm {\mu } \mb{e}\\ \bV \bDelta w_ c + \bW \bDelta v_ c & = - \bV _{\mathit{aff}} \bW _{\mathit{aff}} \mb{e} + \sigma \bm {\mu } \mb{e}\\ \text {where}~ ~ \zeta _{\mathit{start}} = \mb{z}^{\prime } \mb{s} + \mb{v}^{\prime } \mb{w}, & ~ \text {complementarity at the start of the iteration}\\ \zeta _{\mathit{aff}} = \mb{z}_{\mathit{aff}}^{\prime } \mb{s}_{\mathit{aff}} + \mb{v}_{\mathit{aff}}^{\prime } \mb{w}_{\mathit{aff}}, & ~ \text {the affine complementarity}\\ \mu = \zeta _{\mathit{aff}} / 2n, & ~ \text {the average complementarity}\\ \sigma = (\zeta _{\mathit{aff}} / \zeta _{\mathit{start}})^3& \\ \end{align*}