Search results for "test function"
showing 10 items of 10 documents
Wastewater treatment plant design and operation under multiple conflicting objective functions
2013
Wastewater treatment plant design and operation involve multiple objective functions, which are often in conflict with each other. Traditional optimization tools convert all objective functions to a single objective optimization problem (usually minimization of a total cost function by using weights for the objective functions), hiding the interdependencies between different objective functions. We present an interactive approach that is able to handle multiple objective functions simultaneously. As an illustration of our approach, we consider a case study of plant-wide operational optimization where we apply an interactive optimization tool. In this tool, a commercial wastewater treatment …
Bochner-Riesz means of functions in weak-L p
1993
The Bochner-Riesz means of order delta greater-than-or-equal-to 0 for suitable test functions on R(N) are defined via the Fourier transform by (S(R)(delta)f)(xi) = (1 - \xi\2/R2)+(delta)f(xi). We show that the means of the critical index delta = N/P - N + 1/2, 1 + infinity, to f(x) in norm and for almost every x in R(N). We also observe that the means of the function absolute value of x-N/p, which belongs to L(p,infinity) (R(N)) but not to the closure of test functions, converge for no x
The smoothed particle hydrodynamics method via residual iteration
2019
Abstract In this paper we propose for the first time an iterative approach of the Smoothed Particle Hydrodynamics (SPH) method. The method is widespread in many areas of science and engineering and despite its extensive application it suffers from several drawbacks due to inaccurate approximation at boundaries and at irregular interior regions. The presented iterative process improves the accuracy of the standard method by updating the initial estimates iterating on the residuals. It is appealing preserving the matrix-free nature of the method and avoiding to modify the kernel function . Moreover the process refines the SPH estimates and it is not affected by disordered data distribution. W…
Pareto-optimal Glowworm Swarms Optimization for Smart Grids Management
2013
This paper presents a novel nature-inspired multi-objective optimization algorithm. The method extends the glowworm swarm particles optimization algorithm with algorithmical enhancements which allow to identify optimal pareto front in the objectives space. In addition, the system allows to specify constraining functions which are needed in practical applications. The framework has been applied to the power dispatch problem of distribution systems including Distributed Energy Resources (DER). Results for the test cases are reported and discussed elucidating both numerical and complexity analysis.
Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems
2009
Evolutionary multi-objective optimization algorithms are commonly used to obtain a set of non-dominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficient and convergent procedure. In this paper, we test an augmented local search based EMO procedure rigorously on a test suite of constrained and unconstrained multi-objective optimization problems. The success of our approach on most of the test problems not only provides confidence but also stresses the importance of hybrid evolutionary algorithms in solving multi-objective optimization problems.
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B3…
2017
In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.
Hölder Continuity up to the Boundary of Minimizers for Some Integral Functionals with Degenerate Integrands
2007
We study qualitative properties of minimizers for a class of integral functionals, defined in a weighted space. In particular we obtain Hölder regularity up to the boundary for the minimizers of an integral functional of high order by using an interior local regularity result and a modified Moser method with special test function.
Efficient Analysis of Arbitrarily Shaped Inductive Obstacles in Rectangular Waveguides Using a Surface Integral Equation Formulation
2007
In this paper we propose to use the Surface Integral Equation technique for the analysis of arbitrarily shaped Hplane obstacles in rectangular waveguides, which can contain both metallic and/or dielectric objects. The Green functions are formulated using both spectral and spatial images series, whose convergence behavior has been improved through several acceleration techniques. Proceeding in this way, the convergence of the series is not attached to the employment of any particular basis or test function, thus consequently increasing the flexibility of the implemented technique. In order to test the accuracy and numerical efficiency of the proposed method, results for practical microwave c…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …