SVD revisited: A new variational principle, compatible feature maps and nonlinear extensions

A variational principle for nonlinear transport equations

We verify -after appropriate modificationsan old conjecture of Brezis-Ekeland [3] concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of solutions of non-linear transport equations, which do not normally fit in an Euler-Lagrange framework. Our method is based on a concept of “anti-self duality” that seems to be inherent in many problems, i...

$(varphi_1, varphi_2)$-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...

Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

PRINCIPLE AND ITS APPLICATIONS TO NONLINEAR VARIATIONAL PROBLEMS Ram

This paper deals with a crucial role of the partial relaxed monotonicity – a relatively new and less explored concept – in the approximation solvability of a class of nonlinear variational problems on Hilbert spaces, though the convergence analysis much depends on the general auxiliary minimization problem principle. The nonlinear variational inequality problem (NVIP) is stated as follows: find...

On the Relative Variational Principle for Fibre Expanding Maps