Related papers: A Convex Formulation for Mixed Regression with Two…

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a…

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

This paper deals with the problem of estimating the delays and amplitudes of a weighted superposition of pulses, called stream of pulses. This problem is motivated by a variety of applications, such as ultrasound and radar. This paper shows…

The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…

We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a truncated least…

In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…

Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

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 study the problem of reconstructing a block-sparse signal from compressively sampled measurements. In certain applications, in addition to the inherent block-sparse structure of the signal, some prior information about the block support,…

In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…