Updating the price in the model-routing dual

The update is λ_k+1 = [λ_k + α_k(b − a^⊤x_k)]₊. Below the quality target the price rises; above it the price falls. Run with a constant step to watch the routing flip near the kink, then reset and compare the diminishing and Polyak rules.

step rule

α 0.40 λ₀ 0.80 speed

the dual curve, and its value at each iterate current iterate best bound so far p★ = 11 and d★ = 9

iteration k

λ_k

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violation / supergradient s_k

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step α_k

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g(λ_k)

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best bound

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Iteration log