The phrase "analytical optimal" is not grammatically correct.
As adjectives, both "analytical" and "optimal" should be used with a noun that describes the subject of the sentence. For example, you could say "The analytical optimal solution was determined to be the most efficient way forward".
Even given the structure, an analytical optimal solution to the joint optimization problem is still difficult to obtain due to the cross-link interference from the relay node to the destination nodes.
The analogy is reflected at various levels during analytical optimal control computations.
Later, he also provided the analytical optimal solutions for the high-order superdirectivity of circular arrays mounted on a rigid sphere and an infinite rigid cylinder [23].
The purpose of this work is to obtain the analytical optimal design of the reinforcement of a T-section, in terms of the ultimate design.
By resorting to the Lagrangian approach based on the concept of directional derivative, explicit and analytical optimal solutions are obtained in each case under some mild conditions.
The analytical optimal solution for variable factors (left {hat {gamma }_{m}right }_{m=0}^{M-1}) still needs more investigation, and it would be one of our main future research tracks.
Using the analytical results, optimal release lead time and optimal base stock levels for minimizing the average cost on the holding and backlog costs are explicitly derived.
Using the analytical formulae, optimal design charts are constructed to minimize the mass of multilayer sandwich beams for a given low-velocity impact resistance.
The governing partial differential equations are transformed into a set of ordinary differential equations: The non-linear coupled systems of equations have been solved for various values of sundry parameters via an efficient analytical method, optimal homotopy analysis method (OHAM) (for details see Liao (2003), Fan and You (2013)).
A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton Jacobi Bellman (HJB) equation and its variational integral equation, and the finite time element approximation.
Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem.
