An alternative view on the Bateman–Luke variational principle

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

On the Variational Principle

The variational principle states that if a differentiable functional F attains its minimum at some point zi, then F’(C) = 0; it has proved a valuable tool for studying partial differential equations. This paper shows that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F’(uJj* < l , i.e., its de...

An extended variational principle

An Alternative View of Variational Bayes and Minimum Variational Stochastic Complexity

Bayesian learning is widely used in many applied datamodelling problems and is often accompanied with approximation schemes since it requires intractable computation of the posterior distributions. In this study, we focus on the two approximation methods, the variational Bayes and the local variational approximation. We show that the variational Bayes approach for statistical models with latent...

An alternative approach to establishment of a variational principle for the torsional problem of piezoelastic beams

Article history: Received 16 January 2014 Accepted 20 September 2014 Available online 22 October 2014 Submitted by Y. Wei MSC: 15A18 15A57