Related papers: Approximate Regularization Path for Nuclear Norm B…

Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…

Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…

Low-order linear System IDentification (SysID) addresses the challenge of estimating the parameters of a linear dynamical system from finite samples of observations and control inputs with minimal state representation. Traditional…

Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…

In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…

Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…

We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…

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…

In this work we consider the problem of finding optimal regularization parameters for general-form Tikhonov regularization using training data. We formulate the general-form Tikhonov solution as a spectral filtered solution using the…

Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. For linear models, it is…

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear…

We develop regularization methods to find flat minima while training deep neural networks. These minima generalize better than sharp minima, yielding models outperforming baselines on real-world test data (which may be distributed…

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…

This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…