Related papers: Generalized Golub-Kahan bidiagonalization for nons…
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…
This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…
Based on G. Lan's accelerated gradient sliding and general relation between the smoothness and strong convexity parameters of function under Legendre transformation we show that under rather general conditions the best known bounds for…
In the setting of saddle point reduction, we prove that the critical groups of the original functional and the reduced functional are isomorphic. As application, we obtain two nontrivial solutions for elliptic gradient systems which may be…
Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a…
In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or…
Focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid is discussed. For the uniform grid the model sensitivity matrices exhibit block Toeplitz Toeplitz…
We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…
Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean…
We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i)…
Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is…
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…
In this paper we examine iterative methods for solving the forward ($A{\bf x}={\bf b}$) and adjoint ($A^{T}{\bf y}={\bf g}$) systems of linear equations used to approximate the scattering amplitude, defined by ${\bf g}^{T}{\bf x}={\bf…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
The paper considers approaches to saddle point problems with a two-sided variant of the Polyak-Lojasievich condition based on the gradient method with inexact information and proposes a stopping rule based on the smallness of the norm of…
We introduce the nonlinear generalized Collatz-Wielandt formula $$ \lambda^*= \sup_{x\in Q}\min_{i:h_i(x) \neq 0} \frac{g_i(x)}{ h_i(x)}, ~~Q \subset \mathbb{R}^n,$$ and prove that its solution $(x^*,\lambda^*)$ yields the maximal…