Moreover, the equilibrium point set is equivalent to the optimal solution to the nonconvex optimization problem if the objective function and constraints satisfy given conditions.
It can be shown that for a given set of Lagrange multipliers, the subproblems SP1, SP2, and SP3 are constrained integer optimization problem, which is equivalent to the optimal matching problem in the bipartite graph theory, thus can be solved by applying the classical algorithms such as modified K-M algorithm [24].
Based on the EC-PLS, a model set that includes various models equivalent to the optimal model was proposed to select independent and joint-analyses models.
By applying EC-PLS, a model set was developed, which consists of various models that were equivalent to the optimal model.
According to the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the original problem.
It is shown that for all the different system parameters we have explored, this fusion rule is equivalent to the optimal fusion rule, which requires much more prior information.
We remark also that the case when Y is independent of u is equivalent to the optimal transportation case.
From thermodynamic point of view, Stirling cycle is equivalent to the optimal Carnot cycle, having the highest possible efficiency.
We have derived the conditions for optimal training sequences minimizing the MSE of the LMMSE estimator, which is found out to be equivalent to the optimal training conditions of the LS estimator.
These rates were equivalent to the optimal tumour resection rates of type I patients across all stages.
