Related papers: Tensor Based Proximal Alternating Minimization Met…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…

In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…

The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…

Yuan's theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we…

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

It is well-known that accelerated gradient first-order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations it makes sense to work with inexact gradient information.…

We propose a novel non-linear extension to the Orienteering Problem (OP), called the Correlated Orienteering Problem (COP). We use COP to model the planning of informative tours for the persistent monitoring of a spatiotemporal field with…

We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of…

A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without…

In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and…

While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…

This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete…