Standard Forms of SDPA semidefinite program (SDP) is a problem of minimizing a linear function over an LMI constraint.
Standard Inequality FormIn standard inequality form, an SDP is written as ![]() where The above problem generalizes the LP in inequality form: ![]()
Standard Conic FormRecall that we can define the scalar product between two matrices ![]() If In standard conic form, an SDP is written as ![]() where The above generalizes the standard conic form for LP, which can be written as ![]() Just as in LP, the standard inequality and standard conic forms are equivalent, in the sense that we can always convert one into the other, possibly at the expense of introducing new variables and constraints. CVX syntaxIn CVX, a constraint CVX syntax
cvx_begin variables X(n,n) symmetric; minimize( trace(C*X) ) subject to for i = 1:m, trace(A{i}*X == b(i); end X == semidefinite(n); cvx_end |