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The bi-convex matrix factorization problem can be efficiently solved as a sequence of convex sub-problems using an alternating approach.
By the proposed design procedures, the optimal control problems dealt with here can be efficiently solved as Linear Matrix Inequality (LMI) optimization problems.
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They can be efficiently solved by Krylov subspace methods, as here the main ingredient is the multiplication with the system matrix and the application of the preconditioner.
Therefore, the relaxed problem can be efficiently solved using SDP solvers such as SeDuMi [36] or SDPT3 [37].
Therefore, the OP of (24) can be efficiently solved by using optimization tools such as CVX [29].
Note that the problem (14) is an SDP problem which is convex and can, as a result, be efficiently solved using interior-point based solvers [23] at a maximal complexity order of ({mathcal O}big ((K + 2N_{mathrm {r}}^{2} + sum _{k=1}^{K}N_{mathrm {b},k}^{2} + 2)^{3.5}big)) [24].
This method is mathematically formulated as a linear programming, which can be efficiently solved and guarantees a globally optimal solution.
Our aim here is to reformulate this problem as an SDP problem that can be efficiently solved.
Hence, the capacity game can be accurately approached as a standard pursuit-evasion one and be efficiently solved.
The optimization of this criterion can be formulated as a generalized eigenvalue problem that can be efficiently solved.
This can be equivalently written as a standard linear program, which can be "efficiently" solved by the interior-point method [19].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com