Related papers: Bilinear Parameterization For Differentiable Rank-…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving the LM linear system inexactly, subject to specific…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
When solving large scale semidefinite programs that admit a low-rank solution, an efficient heuristic is the Burer-Monteiro factorization: instead of optimizing over the full matrix, one optimizes over its low-rank factors. This reduces the…
Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…
Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…