Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Ambit processes and stochastic partial differential equations
2011
Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Levy noise analysis.
A symmetric nonlocal damage theory
2003
The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present app…
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
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…
Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects
2017
In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.
A product space reformulation with reduced dimension for splitting algorithms
2021
AbstractIn this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assump…
LR-NIMBUS : an interactive algorithm for uncertain multiobjective optimization with lightly robust efficient solutions
2022
In this paper, we develop an interactive algorithm to support a decision maker to find a most preferred lightly robust efficient solution when solving uncertain multiobjective optimization problems. It extends the interactive NIMBUS method. The main idea underlying the designed algorithm, called LR-NIMBUS, is to ask the decision maker for a most acceptable (typical) scenario, find an efficient solution for this scenario satisfying the decision maker, and then apply the derived efficient solution to generate a lightly robust efficient solution. The preferences of the decision maker are incorporated through classifying the objective functions. A lightly robust efficient solution is generated …
Heuristic algorithms for a storage location assignment problem in a chaotic warehouse
2014
The extensive application of emerging technologies is revolutionizing warehouse management. These technologies facilitate working with complex and powerful warehouse management models in which products do not have assigned fixed locations (random storage). Random storage allows the utilization of the available space to be optimized. In this context, and motivated by a real problem, this article presents a model that looks for the optimal allocation of goods in order to maximize the storage space availability within the restrictions of the warehouse. For the proposed model a construction method, a local search algorithm and different metaheuristics have been developed. The introduced algorit…
Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach
2008
We consider the three-dimensional rendezvous between two spacecraft: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular trave…