相关论文: A Two-step Krasnosel'skii-Mann Algorithm with Adap…

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…

The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Recently it was shown by Nesterov (2011) that techniques form convex optimization can be used to successfully accelerate simple derivative-free randomized optimization methods. The appeal of those schemes lies in their low complexity, which…

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

Global motion compensation (GMC) removes the impact of camera motion and creates a video in which the background appears static over the progression of time. Various vision problems, such as human activity recognition, background…

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…

We investigate the convergence of a forward-backward-forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained…

We propose a novel approach to solve K-adaptability problems with convex objective and constraints and integer first-stage decisions. A logic-based Benders decomposition is applied to handle the first-stage decisions in a master problem,…

We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…

Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM)…

We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed…

We present a new approach for nonlocal image denoising, based around the application of an unnormalized extended Gaussian ANOVA kernel within a bilevel optimization algorithm. A critical bottleneck when solving such problems for…

We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a…

Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical…