Second-order cone programming
（重定向自SOCP）
A second-order cone program (SOCP) is a convex optimization problem of the form
where the problem parameters are 
, and 
. Here 
is the optimization variable.
When 
for 
, the SOCP reduces to a linear program. When 
for , the SOCP is equivalent to a convex quadratically constrained linear program. Quadratically constrained quadratic programs can also be formulated as SOCPs by reformulating the objective function as a constraint. Semidefinite programming subsumes SOCPs as the SOCP constraints can be written as linear matrix inequalities (LMI) and can be reformulated as an instance of semi definite program. SOCPs can be solved with great efficiency by interior point methods.