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Semidefinite programming can be regarded as an extension of linear programming. In a semidefinite program, the goal is to optimize a linear function over the intersection of the cone of positive semidefinite matrices with some affine space.
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positive semidefinite matrix condition
There is a great work of Alizadeh that in section 4 speaks about Minimizing sum of the first few(k-largest) eigenvalues of a symmetric matrix. Instead of a symmetric model we use the weighted Laplacia …
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Lagrange multiplier and semidefinite programming
suppose we have a primal semidefinite programming. for finding its dual we use Lagrange multiplier $w_i$ for each semidefinite constraint. If the Lagrange multiplier be zero for one constraint what we …