CVXOPT - primal and dual residuals

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Michael Sommerauer

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Mar 15, 2023, 4:14:41 PM3/15/23

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Hi,

I was looking into the CVXOPT documentation at the feasibility tolerance, specifically for coneqp and I was wondering why the primal and dual residuals are scaled by max(1, ||h||) and max(1, ||q||) respectively?

Cone Programming — CVXOPT User's Guide

Martin

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Mar 20, 2023, 4:33:10 AM3/20/23

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Hi Michael,

Scaling by 1/||h|| and 1/||q|| results in relative residual norms. However, if h or q is the zero vector, then the relative residual norm is undefined. Scaling by 1/max(1,||h||) and 1/max(1,||q||) means that the stopping criteria are either the relative residual norm or the absolute residual norm, depending on ||h|| and ||q||.