To obtain the step length, we have two types of line searches: exact line search as given by (8), which is an expensive line search in terms of calculating the function and gradient evolutions, and inexact line search, which approximates the step length by reducing the function value and direction derivative.
In the function domain, the Pareto front is constituted by the function values of the solutions in the Pareto set.
From a slightly different perspective, the spatial dependence of the coefficients is completely covered by the function values in (W^{1, infty }({{mathbb R}^{N}})), (L^infty ({{mathbb R}^{N}})) and (L^p({{mathbb R}^{N}})), respectively.
If using Excel, add by entering "=Cell1+Cell2" into the function value of the target cell.
However, the optimisation can be parallelised by keeping the members on the master computer and by calculating the function values on several slave computers simultaneously, which was the adopted strategy.
To be more precise, the integration is performed by using the function values which are given as discrete sampling data on only part of the boundary.
The basic idea is to substitute the inner product in the high-dimensional space by the kernel function value of the input vectors to avoid complex calculation procedures of the high-dimensional vectors, i.e., the kernel trick.
It is reasonable to conclude that a model which treats returns as known constants will produce a portfolio whose realized return is different from the optimal portfolio return given by the objective function value.
The principal idea behind DE is to represent the parameters to be optimised as vectors where each vector is a population member whose fitness is described by the cost function value.
