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We can perform semi-definite relaxation through removing rank constraint (19e) [45].
Through removing rank constraint (19e), the problem (19) is now relaxed to maximize tr SW, (26a).
Furthermore, by introducing a rank constraint into KDA, successful ordinal regression can be realized.
The optimization problem is not convex due to rank constraint (19e) and fractional constraint (19b).
To address the issues, the randomization technique is adopted here to solve the rank constraint problem.
Because of the rank constraint the above problem is nonconvex and difficult to solve.
Similar(31)
To make problem (25) tractable, we first ignore the rank constraints and focus on problem (25) without rank constraints named as relaxed problem.
Moreover, explicit rank constraints on state space system matrices are not required.
By applying Lemma 3, problem (19) can be reformulated as an SDP with rank constraints.
Using the S-Procedure[23, 24] this problem with infinitely many constraints can be reformulated as an SDP with rank constraints.
Hence, without the rank constraints the Problem (29) is convex (even when γ is considered as a variable).
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