Self{scaled barrier functions on self{scaled cones were introduced through a set of axioms in 1994 by Y. E. Nesterov and M. J. Todd as a tool for the construction of long{step interior point algorithms. This paper provides rm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of deenition, and subsequently their de...

Self–scaled barrier functions on self–scaled cones were introduced through a set of axioms in 1994 by Y. E. Nesterov and M. J. Todd as a tool for the construction of long–step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of definition, and subsequently their...

Cherenkov radiation (CR) generated by a charge moving through hollow conical target made of dielectric material is analyzed. We consider two cases: the moves from base cone to its top (“straight” cone) or (“inverted” cone). Unlike previous papers, nonzero shift trajectory symmetry axis taken into account, which leads generation asymmetric CR. The most interesting effect phenomenon “Cherenkov sp...

Abstract We propose a new predictor–corrector interior-point algorithm for solving Cartesian symmetric cone horizontal linear complementarity problems, which is not based on usual barrier function. generalize the introduced in Darvay et al. (SIAM J Optim 30:2628–2658, 2020) to problems product of cones. apply algebraically equivalent transformation technique proposed by (Adv Model 5:51–92, 2003...

The geometry of a collector is one of the important factors that can increase the incident radiation on the collector surface. In the present study, the incident radiation for a stationary collector with cone geometry, i.e. a conical collector, is theoretically and experimentally investigated. This type of collector is always stable and does not need a fixture to install. Moreover, it has a...

We study the oblique derivative problem for uniformly elliptic equations on cone domains. Under assumption of axi-symmetry solution, we find sufficient conditions angle vector Hölder regularity gradient to hold up vertex cone. The proof is based application carefully constructed barrier methods or via perturbative arguments. In case that such does not hold, give explicit counterexamples. also a...