Related papers: A Constraint Dissolving Approach for Nonsmooth Opt…

In this paper, we consider a class of structured nonsmooth optimization problems over an embedded submanifold of a Euclidean space, where the first part of the objective is the sum of a difference-of-convex (DC) function and a smooth…

We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We…

We consider the optimization problem of minimizing a nonsmooth function characterized by a nonsmooth formulation of the descent lemma over a manifold. In the unconstrained case over a Euclidean space, this class of functions is called…

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition,…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…

In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…

This paper presents a directional proximal point method (DPPM) to derive the minimum of any C1-smooth function f. The proposed method requires a function persistent a local convex segment along the descent direction at any non-critical…

In this paper, we focus on the nonconvex-strongly-convex bilevel optimization problem (BLO). In this BLO, the objective function of the upper-level problem is nonconvex and possibly nonsmooth, and the lower-level problem is smooth and…

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

Norm-constrained linear minimization oracle (LMO)-based optimizers such as spectral gradient descent and Muon are attractive in large-scale learning, but extending them to manifold-constrained problems is nontrivial and often leads to…

In this paper, we consider a class of stochastic optimization problems over the expectation-formulated generalized Stiefel manifold (SOEGS), where the objective function $f$ is continuously differentiable. We propose a novel constraint…

Nonsmooth Riemannian optimization has attracted increasing attention, especially in problems with sparse structures. While existing formulations typically involve convex nonsmooth terms, incorporating nonsmooth difference-of-convex (DC)…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…