The paper deals with a flow distribution problem with a piecewise-linear cost function. The problem is formulated as a piecewise-linear programming problem which is not separable with respect to separate variable group. The method for solving this problem is based on the extension of the idea of the simplex method to the class of non-separable piecewise-linear problems. It secures finding of a ...

Many statistical analyses can be undertaken to examine the relationship between two continuous variables within a group of subjects. Two of the main purposes of such analyses are: To assess whether the two variables are associated. There is no distinction between the two variables and no causation is implied, simply association. To enable the value of one variable to be predicted from any known...

Efficient Spectral-Galerkin algorithms are developed to solve multi-dimensional fractional elliptic equations with variable coefficients in conserved form as well as non-conserved form. These algorithms are extensions of the spectral-Galerkin algorithms for usual elliptic PDEs developed in [24]. More precisely, for separable FPDEs, we construct a direct method by using a matrix diagonalization ...

Love-type wave generation in a fiber-reinforced medium placed over an inhomogeneous orthotropic half-space is analysed. The upper and lower boundary surfaces of the fiber reinforced medium are periodically corrugated. Inhomogeneity of half-space is caused by variable density and variable shear modules. Displacement components for layer and half-space are derived by applying separable variable t...

8 The training of some types of neural networks leads to separable non-linear least squares problems. These problems may be 9 ill-conditioned and require special techniques. A robust algorithm based on the Variable Projections method of Golub and Pereyra 10 is designed for a class of feed-forward neural networks and tested on benchmark examples and real data.

Variable interaction is an important aspect of a problem, which reflects its structure, and has implications on the design of efficient optimization algorithms. Although variable interaction has been widely studied in the global optimization community, it has rarely been explored in the multi-objective optimization literature. In this paper, we empirically and analytically study the variable in...