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A Hybrid and Inexact Algorithm for Nonconvex and Nonsmooth Optimization
The problem of nonconvex and nonsmooth optimization (NNO) has been extensively studied in the machine learning community, leading to the development...
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Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm
This paper develops an iterative algorithm to solve nonsmooth nonconvex optimization problems on complete Riemannian manifolds. The algorithm is...
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An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms
Nonconvex minimax problems have attracted significant attention in machine learning, wireless communication and many other fields. In this paper, we...
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A proximal bundle method for a class of nonconvex nonsmooth composite optimization problems
In this paper, a proximal bundle method is proposed for a class of nonconvex nonsmooth composite optimization problems. The composite problem...
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Nonsmooth Nonconvex Stochastic Heavy Ball
Motivated by the conspicuous use of momentum-based algorithms in deep learning, we study a nonsmooth nonconvex stochastic heavy ball method and show...
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Stochastic subgradient algorithm for nonsmooth nonconvex optimization
In this paper, we study on a stochastic subgradient algorithm for the finite-sum optimization problems where the functions are not necessarily convex...
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Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems
In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and...
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An Alternating Proximal Gradient Algorithm for Nonsmooth Nonconvex-Linear Minimax Problems with Coupled Linear Constraints
In this paper, we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear...
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General inertial proximal stochastic variance reduction gradient for nonconvex nonsmooth optimization
In this paper, motivated by the competitive performance of the proximal stochastic variance reduction gradient (Prox-SVRG) method, a novel general...
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Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization
This paper is concerned with nonconvex nonsmooth uncertain multiobjective optimization problems, in which the decision variable of both objective and...
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A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems
We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed...
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A Nonconvex Nonsmooth Image Prior Based on the Hyperbolic Tangent Function
In this paper, we propose a nonconvex and nonsmooth image prior based on the hyperbolic tangent function and apply it as a regularization term for...
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An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization
This paper focuses on the minimization of a sum of a twice continuously differentiable function f and a nonsmooth convex function. An inexact...
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Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most...
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On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization
In this work, we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite...
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Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization
In this paper, we consider a proximal linearized alternating direction method of multipliers, or PL-ADMM, for solving linearly constrained nonconvex...
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An alternating structure-adapted Bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant
We consider the nonconvex nonsmooth minimization problem over abstract sets, whose objective function is the sum of a proper lower semicontinuous...
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A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems
In this paper, we consider the problem that minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting, which arising in...
