The (linear) second-order cone program (SOCP) is to minimize a linear function over the intersection
between a polyhedral set and an affine transformation of Cartesian product of second-order
cones. For solving such a problem, the primal-dual interior-point method has been studied extensively
so far and said to be the most efficient method by many researchers. On the other hand,
the simplex type method for SOCP is much less spotlighted, while it still keeps an important position
for linear programming (LP) problems. Actually, some researchers have tried to apply such
a method to the SOCPs. However, in those existing studies, the proposed algorithms were not implemented practically, or could be applied only to some restricted class of problems.
In this paper, we apply the dual-simplex primal-exchange (DSPE) method, which was originally
developed for solving linear semi-infinite programs (LSIP), to the SOCP by reformulating the
second-order cone constraint as an infinite number of linear inequality constraints. Especially,
by means of some numerical experiments, we observe that such a simplex type method can be
more efficient than the existing interior-point based method, when we solve multiple SOCPs having
similar data structures successively applying the so-called hot start technique.