Vakif Dzhafarov | Searcharxiv

arXiv2026

Minimization of a One Class of Maximum Functions with Applications to Some Eigenvalue Problems

In this paper we consider the problem of minimization of a convex function that can be expressed as a maximum of affine linear functions. A convergence theorem is established and the minimizing sequence is constructed. The computational time is linear with respect to the step number. The obtained results are applied to eigenvalue problems such as eigenvalue minimization, symmetric stabilization, and the Riccati matrix inequalities. A number of examples are provided.

math.OC↗

arXiv2018

Pyramidal Polytopes in the Stability Region

Every $n th$ order monic polynomial corresponds $n$-dimensional vector. If the given polynomial is stable that is all its roots lie in the open left half plane it is said to be Hurwitz polynomial and the corresponding vector is called stable vector. The set of stable vectors is non-convex. In this paper, we define special $(n+1) $ stable vectors such that their convex hull is stable.

math.OC↗