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 the perturbation theory of fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality transverse field Ising chain is investigated by second derivative ground-state energy and susceptibility. show that system undergoes a second-order phase transition universal class numerically computing criti...

We study the problem of comparing ageing patterns lifetimes k-out-of-n systems with i.i.d. components. Mathematically, this reduces to being able decide about a stochastic ordering relationship between different order statistics. discuss such relationships respect second-order dominance, obtaining characterizations through verification relative convexity suitably chosen reference distribution f...