The finite element equations are derived for the determination of temperature distribution within a conducting body either by minimizing a suitable functional using a variational (Rayleigh-Ritz) approach or from the governing differential equation using a weighted residual (Galerkin) approach.
Int J Solids Struct 2007 44:895–925] by applying a variational procedure and minimizing a response functional corresponding to the wear-dissipation power.
In this paper, we study a new class of nonconvex multitime multiobjective variational problems of minimizing a vector-valued functional of curvilinear integral type.
We prove that the proposed assimilation method, termed direct assimilation, minimizes a variational functional, a generalized version of the one used in the classical Kalman filter.
Subsequently, we interpret and learn the system using computer vision techniques: First, we present analogies between the system components and computer vision techniques and interpret the network as minimizing a cost functional, thereby establishing a link with variational techniques.
We have exploited these strengths to pursue a simple variational procedure for filter design by minimizing a cost function over the relevant control space.
However, in contrast to conventional algorithms, variational constitutive updates are fully variational, i.e., all unknown variables follow jointly from minimizing a certain potential.
A classical model is the minimizing total variational (TV) functional [8].
This formulation equips the normative account (i.e., minimizing variational free energy or maximizing expected value) with a biologically plausible implementation an implementation that makes some clear predictions about measurable behavioral and neuronal responses.
The complete relaxed state is found by minimizing the total energy, using a variational method.
