First, we show how the problem of minimizing the training energy subject to a quality constraint can be solved, while a 'dual' deterministic (average design) problem is considereda.
It is seen that such a weighted sum-rate problem with more power constraints can be solved by solving a similar problem in (3).
It is well known [11, 12] that the optimization with individual power constraints can be solved by reformulating it properly into an equivalent problem with a sum power constraint.
The vagueness, ambiguities, and uncertainties faced by decision makers from their subjective perceptions and experiences in conducting judgments based on unquantifiable constraints can be solved effectively by using linguistic variables.
Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP).
In fact, the optimization of certain types of non-linear problems can already be solved very efficiently and geometric programming problems with up to 1,000 variables and 10,000 constraints can be solved in minutes on a personal computer.
If G b is non-singular, the magnitudes of the actuation wrenches, the independent constraint wrenches, the resultant constraint wrench, and the resultant constraint couple can be solved from Eq. (13) as {varvec{f}}_{b} = {varvec{G}}_{b}^{ - 1} {not!{varvec{S}}}_{F}.
(15) and (16), the magnitudes of each collinear constraint force and coaxial constraint moment can be solved.
This indicates that the DIND's spatial constraint problem can be solved in the R+iSpace.
Although the new problem is still nonlinear on the boundary, this problem no longer has the inequality constraint and can be solved by the semismooth Newton method with local superlinear convergence rate [7, 14].
