Related papers: Integer Programming Using A Single Atom
A popular approach to sentence compression is to formulate the task as a constrained optimization problem and solve it with integer linear programming (ILP) tools. Unfortunately, dependence on ILP may make the compressor prohibitively slow,…
Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via…
We study the problem of solving Packing Integer Programs (PIPs) in the online setting, where columns in $[0,1]^d$ of the constraint matrix are revealed sequentially, and the goal is to pick a subset of the columns that sum to at most $B$ in…
Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper we explore non-convex boosting in classification by means of integer programming and demonstrate real-world…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem…
In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…