Search results for "nonlinear"
showing 10 items of 3684 documents
Solution isolation strategies for the Bernstein polytopes-based solver
2013
The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perfo…
Sensitivity analysis of consumption cycles
2018
We study the special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional, non-invertible map with an additive stochastic component. Applying the concept of the stochastic sensitivity function and the related technique of confidence domains, we establish the conditions under which the system's complex consumption attractor is likely to become observable. It is shown that the level of noise intensities beyond which the complex consumption attractor is likely to be observed depends on the weight given to past consumption in an individual's preference adjustment.
Transitions in consumption behaviors in a peer-driven stochastic consumer network
2019
Abstract We study transition phenomena between attractors occurring in a stochastic network of two consumers. The consumption of each individual is strongly influenced by the past consumption of the other individual, while own consumption experience only plays a marginal role. From a formal point of view we are dealing with a special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional non-invertible map augmented by additive and/or parametric noise. In our investigation of the stochastic transitions we rely on a mixture of analytical and numerical techniques with a central role given to the concept of the stochastic sensitivity function and the related techni…
Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters
2020
[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution s…
Nonsmooth Penalty Techniques in Control of the Continuous Casting Process
1991
We introduce a mathematical model which is used to simulate the continuous casting process and to control the secondary cooling water sprays. The main object is to minimize the defects in the final products. The problem is formulated as an optimal control problem where the cost function is constructed according to certain metallurgical criteria and constraints. The temperature distribution of the strand is calculated by solving a nonlinear heat equation with free boundaries between solid and liquid phases.
On numerical simulation of the continuous casting process
1988
In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.
SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization
2007
We describe the development and testing of a metaheuristic procedure, based on the scatter-search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-objective problems. However, the application of scatter search to multiobjective optimization problems has not been fully explored in the literature. We test the proposed procedure on a suite of problems that have been used extensively in multiobjective optimization. Additional tests are performed on instances that are an extension of those consid…
On the Extension of the DIRECT Algorithm to Multiple Objectives
2020
AbstractDeterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce r…
Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…
2016
In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…
A linearization technique and error estimates for distributed parameter identification in quasilinear problems
1996
The identification problem of a nonlinear functional coefficient in elliptic and parabolic quasilinear equations is considered. A distributed observation of the solution of the corresponding equation is assumed to be known a priori. An identification method is introduced, which needs only a linear equation to be solved in each iteration step of the optimization. Estimates of the rate of convergence for the proposed approach are proved, when the equation is discretized with the finite element method with respect to space variables. Some numerical results are given.