Related papers: Maximizing the Minimum Eigenvalue in Constant Dime…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…
Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[ M = A\circ X + B…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general $p$-matchoid constraint in the model in which elements of the ground set arrive one…
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 study a bi-objective optimization problem, which for a given positive real number $n$ aims to find a vector $X = \{x_0,\cdots,x_{k-1}\} \in \mathbb{R}^{k}_{\ge 0}$ such that $\sum_{i=0}^{k-1} x_i = n$, minimizing the maximum of $k$…
In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
We study the matroid semi-bandits problem, where at each round the learner plays a subset of $K$ arms from a feasible set, and the goal is to maximize the expected cumulative linear rewards. Existing algorithms have per-round time…
For a Hermitian matrix $H \in \mathbb C^{n,n}$ and symmetric matrices $S_0, S_1,\ldots,S_k \in \mathbb C^{n,n}$, we consider the problem of computing the supremum of $\left\{ \frac{v^*Hv}{v^*v}:~v\in \mathbb C^{n}\setminus…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…