Related papers: On computing with some convex relaxations for the …
We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We derive entropy factorization estimates for spin systems using the stochastic localization approach proposed by Eldan and Chen-Eldan, which, in this context, is equivalent to the renormalization group approach developed independently by…
The 0/1 D-optimality problem and the Maximum-Entropy Sampling problem are two well-known NP-hard discrete maximization problems in experimental design. Algorithms for exact optimization (of moderate-sized instances) are based on…
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…
This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
This paper addresses the challenge of solving Constrained Markov Decision Processes (CMDPs) with $d > 1$ constraints when the transition dynamics are unknown, but samples can be drawn from a generative model. We propose a model-based…
In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming (MIP) relaxations.…
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set $\{x \in \mathcal{X}: c(x) = 0\}$, where $\mathcal{X}$ is a closed convex subset of $\mathbb{R}^n$. Building upon the forward-backward…