  We compute the reduced electric-dipole matrix elements
$\langle{nS_{1/2}}||D||{n'P_J}\rangle$ with $n=6,7$ and $n'=6,7,\ldots,12$ in
cesium using the most complete to date ab initio relativistic coupled-cluster
method which includes singles, doubles, perturbative core triples, and valence
triples. Our results agree with previous calculations at the linearized single
double level but also show large contributions from nonlinear singles and
doubles as well as valence triples. We also calculate the normalized ratio
$\xi_{n,n'}\equiv(1/\sqrt{2})\langle{nS_{1/2}}||D||{n'P_{1/2}}\rangle/\langle{nS_{1/2}}||D||{n'P_{3/2}}\rangle$
which is important for experimental determination of matrix elements. The
ratios $\xi_{6,n}$ display large deviations from the nonrelativistic limit
which we associate with Cooper-like minima. Several appendices are provided
where we document the procedure for constructing finite basis sets and our
implementation of the random phase approximation and Brueckner-orbitals method.
