相关论文: Incremental Algorithms for Lattice Problems

We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…

In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing…

A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a…

We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…

The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter…

In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…

The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained class of operators based on prior information with low bias, and low complexity relative to the…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…

We present an algorithmic contribution to improve the efficiency of robust trim-fitting in outlier affected geometric regression problems. The method heavily relies on the quick sort algorithm, and we present two important insights. First,…

This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…

Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…

Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…

We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…