We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...

Direct algebraic method of obtaining exact solutions to nonlinear PDE’s is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.

As an emerging non-parametric modeling technique, the methodology of support vector regression blazed a new trail in identifying complex nonlinear systems with superior generalization capability and sparsity. Nevertheless, the conventional quadratic programming support vector regression can easily lead to representation redundancy and expensive computational cost. In this paper, by using the no...

Abstract— A generalization of the L2-gain inequality based on nonlinear gains is considered. Using optimization and dynamic programming to characterize lower bounds for the minimal gain function for which this nonlinear L2-gain inequality holds, a technique for computation of nonlinear L2gain bounds is proposed. Some simple illustrative examples are explored.

The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation poten...

Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. “Faster-than-light telegraphs” are absent for all theories formulated within the new framework. A new metric for infinite dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

Steel consumption is a critical factor affecting pricing decisions and a key element to achieve sustainable industrial development. Forecasting future trends of steel consumption based on analysis of nonlinear patterns using artificial intelligence (AI) techniques is the main purpose of this paper. Because there are several features affecting target variable which make the analysis of relations...

This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including cohomology and Hodge theory. At the end we will also discuss the nonlinear Laplacian on a graph, a nonlinear generalization of the graph Laplacian as its name implies. These generalized Laplacians will be constructed out of coboun...

In this paper a generalization of Post Nonlinear Independent Component Analysis (PNL-ICA) to Post Nonlinear Independent Subspace Analysis (PNL-ISA) is presented. In this framework sources to be identified can be multidimensional as well. For this generalization we prove a separability theorem: the ambiguities of this problem are essentially the same as for the linear Independent Subspace Analys...

The selection of input variables plays a crucial role when modelling time series. For nonlinear models there are not well developed techniques such as AIC and other criteria that work with linear models. In the case of Short Term Load Forecasting (STLF) generalization is greatly influenced by such selection. In this paper two approaches are compared using real data from a Spanish utility compan...