The Lagrange dual function is obtained by convex conjugate definition and the dual problem is solved using gradient ascent.
For this purpose, the LED transmitters are modeled as fixed points in a color space, and the constellation symbols are obtained by convex combinations of these points.
In the present study they are determined to produce the least favourable initial deflection (largest deflection) at a given point and the solution is obtained by convex modelling.
Furthermore, with the mentioned indices constraints, a solution is obtained by convex optimal technique for the robust satisfactory fault-tolerant controller with optimal control-cost.
Analyzed by a numerical example, the width of the upper and lower bounds of the critical buckling loads that calculated by the interval analysis method is sharper than those are obtained by convex models.
We argue that a greater variety can be obtained by using convex polyhedra as bounding volumes instead.
The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays.
Then, the Lp-norm minimization method is applied to design digital wideband FHT whose solution can be obtained by using convex optimization tool.
The claim that the function s ↦ Φ i ( x, y ; p, g, f s ) is log-convex on I is an immediate consequence of Theorem 3.7 and Remark 3.5, and (24) can be obtained by replacing the convex function f with the convex function f ( z ) = log Φ i ( x, y ; p, g, f z ) for z = r, s, t in (21), where r, s, t ∈ I such that r < s < t.
In addition, it can be verified that the optimization problem (8a) and (8b) is convex; therefore, its optimal solution can be obtained by any standard convex optimization algorithm.
Moreover, the minimum attenuation level bound can be obtained by solving a convex optimization problem.
