  For approximate inference in high-dimensional generalized linear models
(GLMs), the performance of an estimator may significantly degrade when mismatch
exists between the postulated model and the ground truth. In mismatched GLMs
with rotation-invariant measurement matrices, Kabashima et al. proved vector
approximate message passing (VAMP) computes exactly the optimal estimator if
the replica symmetry (RS) ansatz is valid, but it becomes inappropriate if RS
breaking (RSB) appears. Although the one-step RSB (1RSB) saddle point equations
were given for the optimal estimator, the question remains: how to achieve the
1RSB prediction? This paper answers the question by proposing a new algorithm,
vector approximate survey propagation (VASP). VASP derives from a reformulation
of Kabashima's extremum conditions, which later links the theoretical equations
to survey propagation in vector form and finally the algorithm. VASP has a
complexity as low as VAMP, while embracing VAMP as a special case. The SE
derived for VASP can capture precisely the per-iteration behavior of the
simulated algorithm, and the SE's fixed point equations perfectly match
Kabashima's 1RSB prediction, which indicates VASP can achieve the optimal
performance even in a model-mismatched setting with 1RSB. Simulation results
confirm VASP outperforms many state-of-the-art algorithms.
