Related papers: Towards a geometric characterization of unbounded …
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…
Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
In this note we show that unbounded convex polygons with nonparallel unbounded edges are polynomial images of ${\mathbb R}^2$, whereas their interiors are polynomial images of ${\mathbb R}^3$
In the current paper we are seeking P1(y),P2(y),P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that P1(y)^3+P2(y)^3+P3(y)^3=Q(y). Actually, the solution…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…