Related papers: An Efficient Augmented Lagrangian Method with Semi…
Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…
We propose a semismooth Newton-based augmented Lagrangian framework for reconstructing sparse sources in inverse acoustic scattering problems. Rather than working in the unknown source space, our semismooth Newton updates operate in the…
We consider a multi-block separable convex optimization problem with the linear constraints, where the objective function is the sum of m individual convex functions without overlapping variables. The linearized version of the generalized…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
We propose NAMA (Newton-type Alternating Minimization Algorithm) for solving structured nonsmooth convex optimization problems where the sum of two functions is to be minimized, one being strongly convex and the other composed with a linear…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…
The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive…
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…
This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is…
In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
This is a documentation of a framework for robot motion optimization that aims to draw on classical constrained optimization methods. With one exception the underlying algorithms are classical ones: Gauss-Newton (with adaptive step size and…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…
Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…