Related papers: Erd\H{o}s' minimum overlap problem
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz…
A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work.…
Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay…
Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. In this paper we prove an upper bound on the minimal…
Theoretical results show that sparse off-the-grid spikes can be estimated from (possibly compressive) Fourier measurements under a minimum separation assumption. We propose a practical algorithm to minimize the corresponding non-convex…
For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
To every nearly convex optimization problem, that is a minimization problem with a nearly convex objective function and a nearly convex constraint set, we associate a uniquely defined convex optimization problem with a lower semicontinuous…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…
We introduce a $2$-approximation algorithm for the minimum total covering number problem.
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
We present two short proofs giving the best known asymptotic lower bound for the maximum element in a set of $n$ positive integers with distinct subset sums.