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Check forwarding for reliability constraints (18) and (19).
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In conjunction with an efficient adjoint variable scheme for the sensitivity analysis of reliability constraints, the optimization problem is solved by gradient-based mathematical programming methods.
In each sub-programming, rather than direct Taylor expansion of reliability constraints, a new formulation is introduced for approximate reliability constraints at the current design point and its linearization.
The reliability-based topology optimization (RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints.
{ γ i } i = 1 K is the set of the predefined values which are used for the proportional reliability constraints.
The optimal power distribution uses the exact BER expressions given by [33] instead of the derived BER upper bounds for the proportional reliability constraints.
Similarly, the analysis can be also applied to ϖ i, i = 2,..., K which are associated with the proportional reliability constraints for the ELs.
This is then used within an optimization algorithm for minimum total cost under reliability constraints.
Moreover, it is also revealed that the geometrical nonlinearity needs to be accounted for to ensure satisfaction of the reliability constraints in the optimal design of structures with large deformation.
The on-chip ESD protection circuit for mixed-voltage I/O interfaces should meet the gate-oxide reliability constraints and prevent the undesired leakage current paths.
Traditionally for these problems, the objective function is to minimize a cost function while satisfying the reliability constraints.
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