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We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds.
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Existence conditions for the control structure can be cast as (convex) optimization problems over Linear Matrix Inequalities.
Existence conditions for these two control structures can be cast as (convex) optimization problems over linear matrix inequalities (LMIs).
Therefore, the basic operation can be cast as an optimization problem which is expressed as follows begin{array}{l}kern1.2em min {mathbf{w}}_akern2.1em Eleft[{leftVert {mathbf{w}}_m^H{mathbf{x}}_m(t -{mathbf{w}}_a^H{mat -{mathbf{w}rightVert}_a^H{mathbf{x}m{subject}_arn0.4em mathrightVertrm{o}^2rightem {mathbf{w}}_a^H{mathbf{a}}_{a,0}left({theta}_0^{prime}right)=0end{array} (6).
The anti-windup design problem can be cast as an LMI optimization problem.
We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently.
For systems with symmetric dynamic matrices, the problem of minimizing the H2 or H∞ performance of the closed-loop system can be cast as a convex optimization problem.
Local rule design for this two-stage strategy can be cast as a constrained optimization problem with a Bayesian risk capturing the cost of transmissions and penalty for the estimation errors.
Accordingly, it is demonstrated that this problem can be cast as a convex optimization problem in which the individual power constraints are tackled by employing the method of Lagrange multipliers in two stages.
This problem thus can be cast as the following optimization: {text{SINR}_{Omega_{text{best}}}}= maxlimits_{Omega_{r q)}} {text{min}({mathrm{{SINR}_{Omega_{r q)}}}}), q=1,ldots,K}, (34).
Thus, due to the composite combinations (hypotheses over hypotheses with cascade interlaces, as in the cases of hypotheses H9,…, H12), the proper selection of the preferable implementation structure cannot be cast as an analytically tractable closed-form optimization problem.
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