相关论文: Variational Analysis of Kurdyka-{\L}ojasiewicz Pro…

Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of $\frac12$ for a suitable potential function is related to local linear…

In this paper, we study the Kurdyka-{\L}ojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly…

Kurdyka-{\L}ojasiewicz (K{\L}) functions are real-valued functions characterized by a differential inequality involving the norm of their gradient. This class of functions is quite rich, containing objects as diverse as subanalytic,…

We introduce a generalized version of the concave Kurdyka-\L ojasiewicz (KL) property by employing nonsmooth desingularizing functions. We also present the exact modulus of the generalized concave KL property, which provides an answer to…

We devise calculus rules for the Kurdyka-\L{}ojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local…

We consider a class of $\ell_1$-regularized optimization problems and the associated smooth "over-parameterized" optimization problems built upon the Hadamard parametrization, or equivalently, the Hadamard difference parametrization (HDP).…

This paper focuses on a class of zero-norm composite optimization problems. For this class of nonconvex nonsmooth problems, we establish the Kurdyka-Lojasiewicz property of exponent being a half for its objective function under a suitable…

We consider one of the most common reparameterization techniques, the square transformation. Assuming the original objective function is the sum of a smooth function and a polyhedral function, we study the variational properties of the…

A central tool for understanding first-order optimization algorithms is the Kurdyka-Lojasiewicz inequality. Standard approaches to such methods rely crucially on this inequality to leverage sufficient decrease conditions involving gradients…

We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…

This work extends the iterative framework proposed by Attouch et al. (in Math. Program. 137: 91-129, 2013) for minimizing a nonconvex and nonsmooth function $\Phi$ so that the generated sequence possesses a Q-superlinear convergence rate.…

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems:…

We study the convergence properties of the 'greedy' Frank-Wolfe algorithm with a unit step size, for a convex maximization problem over a compact set. We assume the function satisfies smoothness and strong convexity. These assumptions…

In this paper, we propose several calculus rules for the generalized concave Kurdyka-\L ojasiewicz (KL) property, which generalize Li and Pong's results for KL exponents. The optimal concave desingularizing function has various forms and…

We incorporate an iteratively reweighted strategy in the manifold proximal point algorithm (ManPPA) in [12] to solve an enhanced sparsity inducing model for identifying sparse yet nonzero vectors in a given subspace. We establish the global…

Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorithms generate iterates in discrete time that are eventually…

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: $L(x,y)=f(x)+Q(x,y)+g(y)$, where $f:\R^n\rightarrow\R\cup{+\infty}$ and $g:\R^m\rightarrow\R\cup{+\infty}$…

We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--\L ojaziewicz (KL) inequality we establish new convergence rates…

This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-{\L}ojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by…

We study the random reshuffling (RR) method for smooth nonconvex optimization problems with a finite-sum structure. Though this method is widely utilized in practice such as the training of neural networks, its convergence behavior is only…