For semidefinite programming (SDP), we have the primal and dual forms as:
primal
min <C,X>
s.t. <A_i,X> = b_i, i=1,...,m
X>=0
dual
max <b,y>
s.t. y_1*A_1 + ... + y_m*A_m <=C
where the data A_i and C are assumed to be real symmetric matrices in many textbooks and online...