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Smooth over-parameterized solvers for non-smooth structured optimization
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the...
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Efficient Convex Optimization for Non-convex Non-smooth Image Restoration
This work focuses on recovering images from various forms of corruption, for which a challenging non-smooth, non-convex optimization model is...
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Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization
Stochastic composite objective mirror descent (SCOMID) is an effective method for solving large-scale stochastic composite problems in machine...
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Barcodes as Summary of Loss Function Topology
AbstractWe propose to study neural networks’ loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes...
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Non-smooth atomic decomposition of Triebel–Lizorkin-type spaces
In this article, the authors establish a non-smooth atomic decomposition of Triebel–Lizorkin-type spaces and, as a by-product, a non-smooth atomic...
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An Invitation to Optimality Conditions Through Non-smooth Analysis
In this short article, we show the fundamental role that non-smooth analysis plays in devising optimality conditions. Written with the graduate...
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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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A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...
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Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems
In this paper, we consider a class of possibly non-convex and non-smooth optimization problems arising in many contemporary applications such as...
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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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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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Invariant rectification of non-smooth planar curves
We consider the problem of defining arc length for a plane curve invariant under a group action. Initially one partitions the curve and sums a...
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Subharmonic Bifurcation for a Non-smooth Double Pendulum with Unilateral Impact
A unilateral impact double pendulum model with hinge links is constructed to detect subharmonic bifurcation for the high dimensional non-smooth...
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Optimality conditions and Lipschitz stability for non-smooth semilinear elliptic optimal control problems with sparse controls
This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control...
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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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Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity
With the help of bounded metric subregularity which is weaker than strong convexity, we show the linear convergence of proximal stochastic...
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Some non-smooth optimality results for optimization problems with vanishing constraints via Dini–Hadamard derivative
This research examines a wide class of optimization problems that are known in the literature as mathematical programs with vanishing constraints...
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Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement
The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels...
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A Calculus for Non-smooth Shape Optimization with Applications to Geometric Inverse Problems
We are concerned with a class of non-smooth shape optimization problems involving the total variation of the normal vector field along the shape’s...