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Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems
Motivated by a recent framework for proving global convergence to critical points of nested alternating minimization algorithms, which was proposed...
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Unadjusted Langevin Algorithm for Non-convex Weakly Smooth Potentials
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama...
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Gradient-free Federated Learning Methods with l1 and l2-randomization for Non-smooth Convex Stochastic Optimization Problems
AbstractThis paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the...
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Optimal semiclassical spectral asymptotics for differential operators with non-smooth coefficients
We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two-term optimal...
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An Arnold-type principle for non-smooth objects
In this article, we study the Arnold conjecture in settings where objects under consideration are no longer smooth but only continuous. The example...
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Convergence of Constant Step Stochastic Gradient Descent for Non-Smooth Non-Convex Functions
This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function, defined as...
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Non-smooth Bifurcations
In this chapter we will be interested in bifurcations that result from two “non-smooth” phenomena:...
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Trilevel and multilevel optimization using monotone operator theory
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints...
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Discrete-to-Continuous Extensions: Lovász Extension and Morse Theory
This is the first of a series of papers that develop a systematic bridge between constructions in discrete mathematics and the corresponding...
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Planar Equilibrium Measure Problem in the Quadratic Fields with a Point Charge
We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit...
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Critical Points of Potential Functions and Floer Cohomology
In this chapter, with the analysis of one-point open Gromov–Witten invariants given in the previous section at our disposal, we develop the critical...
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Multiparameter discrete Morse theory
The main objective of this paper is to extend Morse–Forman theory to vector-valued functions. This is mostly motivated by the need to develop new...
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Local generic behavior of a planar Filippov system with non-smooth switching curve
This paper discusses the generic local classification of typical singularities of 2 D piecewise smooth vector fields when the switching set is an non...
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Super-Explosion and Inverse Canard Explosion in a Piecewise-Smooth Slow–Fast Leslie–Gower Model
In this paper, we study a slow–fast Leslie-type predator–prey model with piecewise-linear functional response. Our approach is based on the geometric...
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An Arnold-type prinicple for non-smooth objects
In this article, we study the Arnold conjecture in settings where objects under consideration are no longer smooth but only continuous.
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Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds
This paper studies the convergence of the proximal point method for quasiconvex functions in finite dimensional complete Riemannian manifolds. We...
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Symmetric Semi-perfect Obstruction Theory Revisited
In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne—Mumford stack X constructed by Chang—Li, and...
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Critical Points of Solutions to Exterior Boundary Problems
In this article, we mainly study the critical points of solutions to the Laplace equation with Dirichlet boundary conditions in an exterior domain in...