Furthermore, it is getting feasible more and more because of the cost reduction of energy storage system, such as lithium-ion battery, in Japan.
Because the dual solution is not necessarily primal feasible, we also present an algorithm to get a feasible point from the dual solution, which is a lower bound to the optimal primal solution.
By solving LMIs (5)–(10), we get the feasible solutions.
By ironing algorithm, we get a feasible solution of the problem (Equation 12).
There exist many real-life problems that consider multiple objectives, and generally, it is very difficult to get a feasible solution that brings us to the optimum of all the objective functions.
Considering the synchronization of this master-slave system and choosing μ = − 1, τ = 0, after computing by the LMI's Toolbox in the Matlab, one can get the feasible solutions of inequalities (5) and (6) as follows: P = diag { 1, 1, 1 }, L 1 ∗ = 4, L 2 ∗ = 1.1.
From what has been described above, we easily get the feasible strategy set of Fi as (S_{i}={A_{1}=(4,0),A_{2}= 3,0),A_{3}=(2,1),A_{4}=(1,2),A_{5}= 0,2)}), where the first and second components of (A_{k}) with (k in{1,2,ldots,5}) denote the number of tankers and the number of fighter planes produced by Fi, respectively.
During the optimization trails with the tolerance adjustment, we get a feasible point that may be a more suitable initial guess for the next trial.
