SDP stands for Semi-Definite Programming.

SDP is a generatization of Linear Programming (LP) and Second Order Cone Programming (SOCP) to the cone of positive semidefinite matrices.

Basically, a SDP problem is a LP problem where the positivity constraint is replaced by a semidefinite positivity constraint on the matrix X. The standard form of the primal problem is:

Min_x trace(CX)    s.t.   X є C_n and trace (A_iX) = b_i ,  i=1,...,N

where C_n is the convex cone of semidefinite positive matrices, also called Semidefinite Cone.

SDP differs from LP and SOCP in the type of conic constraints. Whereas LP and SOCP constraints lie respectively within the positive orthant and the Lorentz cone, SDP constraints are semidefinite cone constraints.

A wide range of optimization problems in finance can be cast as SDP problems, such as portfolio optimization problems, model calibration and matrix calibration.