Search results for "nonlinear optimization"

Cooperative spectrum sensing schemes for future dynamic spectrum access infrastructures

2016

Chebyshev’s Method on Projective Fluids

2020

We demonstrate the acceleration potential of the Chebyshev semi-iterative approach for fluid simulations in Projective Dynamics. The Chebyshev approach has been successfully tested for deformable bodies, where the dynamical system behaves relatively linearly, even though Projective Dynamics, in general, is fundamentally nonlinear. The results for more complex constraints, like fluids, with a particular nonlinear dynamical system, remained unknown so far. We follow a method describing particle-based fluids in Projective Dynamics while replacing the Conjugate Gradient solver with Chebyshev’s method. Our results show that Chebyshev’s method can be successfully applied to fluids and potentially…

Interactive Nonlinear Multiobjective Optimization Methods

2016

An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the role of the decision maker is very important in interactive methods, methods presented are classified according to the type of preference information that the decision maker is assumed to provide. peerReviewed

DESDEO: The Modular and Open Source Framework for Interactive Multiobjective Optimization

2021

Interactive multiobjective optimization methods incorporate preferences from a human decision maker in the optimization process iteratively. This allows the decision maker to focus on a subset of solutions, learn about the underlying trade-offs among the conflicting objective functions in the problem and adjust preferences during the solution process. Incorporating preference information allows computing only solutions that are interesting to the decision maker, decreasing computation time significantly. Thus, interactive methods have many strengths making them viable for various applications. However, there is a lack of existing software frameworks to apply and experiment with interactive …

A nonlinear optimization procedure to estimate GTR-distances

2006

On FE-grid relocation in solving unilateral boundary value problems by FEM

1992

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed