Related papers: Evaluating the Gilbert-Varshamov Bound for Constra…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1) where V(n,d) stands for the volume of a Hamming ball of radius d. Recently Jiang and…
We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…
A family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant. The asymptotic quantum Gilbert-Varshamov (GV) bound states that…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
We address a class of integer optimization programs with a total variation-like regularizer and convex, separable constraints on a graph. Our approach makes use of the Graver basis, an optimality certificate for integer programs, which we…
An algorithm to determine all the Gromov-Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…
We consider the celebrated bound introduced by Conforti and Cornu\'ejols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy…
We introduce and study VERSs (vertex and edge replacement systems) as a technology of graph expansions. We consider its history graph, an augmented tree that records each graph expansion, and we provide sufficient conditions under which it…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
Stochastic optimization algorithms are widely used for large-scale data analysis due to their low per-iteration costs, but they often suffer from slow asymptotic convergence caused by inherent variance. Variance-reduced techniques have been…
This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This…