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Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
By concisely representing a joint function of many variables as the combination of small functions, discrete graphical models (GMs) provide a powerful framework to analyze stochastic and deterministic systems of interacting variables. One…
Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm…
This paper aims to answer an open question recently posed in the literature, that is to find a fast exact method for solving the p-dispersion-sum problem (PDSP), a nonconcave quadratic binary maximization problem. We show that, since the…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
We study the Heilbronn triangle problem, which involves placing n points in the unit square such that the minimum area of any triangle formed by these points is maximized. A straightforward maximin formulation of this problem is highly…
Estimating singular subspaces from noisy matrices is a fundamental problem with wide-ranging applications across various fields. Driven by the challenges of data integration and multi-view analysis, this study focuses on estimating shared…
We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. An instance of the problem Max (r,2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n…
Let us consider the following robust nonconvex quadratic optimization problem: \begin{equation*} \begin{split} \min &~ \dfrac{1}{2} x^\top Ax+a^\top x \\ \text{s.t.}~ & \alpha\leq\dfrac{1}{2}x^\top (B_1+\mu B_2)x+(b_1+\delta b_2)^\top x…
We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…
We develop an efficient algorithm for weak recovery in a robust version of the stochastic block model. The algorithm matches the statistical guarantees of the best known algorithms for the vanilla version of the stochastic block model. In…
We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli…
In this paper we consider a minimization problem of the type $$ I_{\beta,p}(D;\Omega)=\inf\biggl\{\int_\Omega \lvert{D\phi}\rvert^pdx+\beta \int_{\partial^* \Omega}\lvert{\phi}\rvert^pd\mathcal{H}^{n-1},\; \phi \in W^{1,p}(\Omega),\;\phi…
Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent $M$-ary phase-shift keying ($M$PSK) sequence detection, result in the maximization of a fixed-rank positive…