35 citations · 77 across the 7 of their papers we have counts for
8 papers
Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds
Maxim Balashov, Andrey Tremba
We analyse the convergence of the gradient projection algorithm, which is finalized with the Newton method, to a stationary point for the problem of nonconvex constrained optimizat…
Gradient projection and conditional gradient methods for constrained nonconvex minimization
Maxim Balashov, Boris Polyak, Andrey Tremba
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is t…
On Pliś metric on the space of strictly convex compacta
Maxim V. Balashov, Dušan Repovš
We consider a certain metric on the space of all convex compacta in , introduced by A. Pliś. The set of strictly convex compacta is a complete metric subspace of the metric…
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Maxim V. Balashov, Dušan Repovš
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obta…
Polyhedral approximations of strictly convex compacta
Maxim V. Balashov, Dušan Repovš
We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible esti…
Weakly convex sets and modulus of nonconvexity
Maxim V. Balashov, Dušan Repovš
We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clar…