Fix factor-2 error in Hermitian PSD constraint dual recovery#3388
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Fix factor-2 error in Hermitian PSD constraint dual recovery#3388PTNobel wants to merge 1 commit into
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A Hermitian PSD constraint X >> 0 is canonicalized to the real dilation [[Re(X), -Im(X)], [Im(X), Re(X)]] >> 0. The dilation doubles the inner product: <Y_big, X_big> = 2*Re(<Y, X>) for Y recovered from the blocks of Y_big. Complex2Real.invert() recovered the complex dual as dual[:n,:n] + 1j*dual[n:,:n] without compensating, so Hermitian PSD duals were half their correct value: for minimize Re(trace(C @ X)) s.t. X >> A the KKT conditions give Y == C, but con.dual_value returned C/2 and violated strong duality (Re(<Y, A>) was half the optimal value). The real symmetric analog already returned the correct dual. Multiply the recovered dual by 2. Other complex dual recoveries in complex2real.py (Equality/Zero and purely imaginary constraints) split into separate real constraints rather than a dilation, so they have no such factor and are unchanged. No existing tests encoded the halved value. The regression test checks the dual equals C and that strong duality holds; the fix was also verified against finite-difference sensitivity to Hermitian perturbations of A. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Description
A Hermitian PSD constraint X >> 0 is canonicalized to the real
dilation [[Re(X), -Im(X)], [Im(X), Re(X)]] >> 0. The dilation doubles
the inner product: <Y_big, X_big> = 2Re(<Y, X>) for Y recovered from
the blocks of Y_big. Complex2Real.invert() recovered the complex dual
as dual[:n,:n] + 1jdual[n:,:n] without compensating, so Hermitian PSD
duals were half their correct value: for
minimize Re(trace(C @ X)) s.t. X >> A the KKT conditions give Y == C,
but con.dual_value returned C/2 and violated strong duality
(Re(<Y, A>) was half the optimal value). The real symmetric analog
already returned the correct dual.
Multiply the recovered dual by 2. Other complex dual recoveries in
complex2real.py (Equality/Zero and purely imaginary constraints) split
into separate real constraints rather than a dilation, so they have no
such factor and are unchanged. No existing tests encoded the halved
value.
The regression test checks the dual equals C and that strong duality
holds; the fix was also verified against finite-difference sensitivity
to Hermitian perturbations of A.
Found by an automated bug-hunting audit of master; each finding was reproduced against an independent oracle before fixing.
Type of change
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