arXiv subjects

D. Kamburova

Publications and source records attributed to D. Kamburova.

3 recordsLinked to original sources

arXiv2026

Generic variational principles for supinf problems with constraints

We study supinf problems for perturbations of a given function of two variables by continuous bounded functions in the underlying spaces and the properties of the associated solution mapping. We provide conditions on the initial data such that most (in the Baire category sense) of the functions from the perturbation space secure existence and uniqueness of the solution of the supinf problem for the corresponding perturbed functions. In this way we obtain generic variational principles for such problems.

math.FA↗

arXiv2025

On Long Orbit Empty Value (LOEV) principle

We consider an useful in Variational Analysis tool -- Long Orbit or Empty Value (LOEV) principle -- in different settings, starting from more abstract to more defined. We prove, using LOEV principle, a number of basic results in Variational Analysis, including some novel. We characterize $Σ_g$-semicompleteness for a generalized metric function $g$ which is neither symmetric nor satisfies the triangle inequality, in terms of validity of Ekeland Theorem for this $g$. We present an interesting application to perturbability to minimum in a $G_δ$ subset of a complete metric space.

math.FA↗

arXiv2023

Saddle points in completely regular topological spaces

We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle point problems is studied as well.

math.OC↗