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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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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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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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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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Zero-Order Stochastic Conditional Gradient Sliding Method for Non-smooth Convex Optimization
The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also...
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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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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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Inertial alternating direction method of multipliers for non-convex non-smooth optimization
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of...
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Algorithms Based on Abs-Linearization for Non-smooth Optimization with PDE Constraints
This chapter presents two optimization algorithms to solve non-smooth optimization problems subject to PDE constraints. Throughout, all...
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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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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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Applications of Conic Programming in Non-smooth Mechanics
In the field of nonlinear mechanics, many challenging problems (e.g., plasticity, contact, masonry structures, nonlinear membranes) turn out to be...
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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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Non-Smooth and Complementarity-Based Distributed Parameter Systems Simulation and Hierarchical Optimization
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus...
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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 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...
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A fast continuous time approach for non-smooth convex optimization using Tikhonov regularization technique
In this paper we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the...
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Noisy Zeroth-Order Optimization for Non-smooth Saddle Point Problems
This paper investigates zeroth-order methods for non-smooth convex-concave saddle point problems (with r-growth condition for duality gap). We...
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On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces
In this paper, the convergence of the fundamental alternating minimization is established for non-smooth non-strongly convex optimization problems in...
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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...
