This paper demonstrates that, unlike in AC grids, convergence and uniqueness of the solution can be guaranteed in this type of grid under well defined practical considerations.
Actually, most of the resulting problems of joint beamforming and power control are inherently non-convex, and consequently, no global optimality of an efficient solution can be guaranteed theoretically [20].
Compared with traditional SE methods based on (2) (including MINP model), (8) is a MILP problem, thus it possesses the following advantages: ① the global optimal solution can be guaranteed mathematically; ② there is no convergence problem for (8); ③ it can effectively suppress bad measurements (including leverage bad measurements), which will be proved by the tests in the next section.
The GMEC solution can be guaranteed by GSMA*768 on all our test data even if we only used ∼10% of memory required by GA*768.
When designing dynamic neural networks, it is important to know whether steady state solutions can be guaranteed.
Computational experiments reveal, that although no optimal solutions can be guaranteed, the approach provides promising results, both regarding practical applicability and further research potential.
With the proposed two-step formulation, one can integrate information theory conveniently to supervise the feature selection process while the optimal solutions can be guaranteed due to the convex optimization formulations in a generalized lasso framework.
Although the equations that have to be solved to design the controller consist of the nonlinear cross-coupled algebraic Riccati equations (CAREs), it is newly proven that both the uniqueness and the positive semidefiniteness of the iterative solutions can be guaranteed when disturbance attenuation level γ is sufficiently large.
The existence and uniqueness of solutions to (2.5 - 2.6) can be guaranteed by the theory in [19].
The existence of at least one solution to problem (1.1) can be guaranteed by imposing pseudomonotonicity and coercivity conditions on the mapping (A_{0}) (see, for example, [2, 3]).
When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion.
