This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such considered both exact inexact forms. Using generalized differential tools variational analysis, we formulate corresponding version sufficiency use it establish, among other results, uniform growth condition...

We develop a theoretical tool to examine the properties of numerical schemes for advection equations. To magnify the defects of a scheme we consider a convection-reaction equation 0021-9 doi:10. q Th * Co E-m ut þ ðjujq=qÞx 1⁄4 u; u; x 2 R; t 2 Rþ; q > 1: It is shown that, if a numerical scheme for the advection part is performed with a splitting method, the intrinsic properties of the scheme a...

The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted ...

In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...