Maximizing Polynomials Subject to Assignment Constraints
We study the q-adic assignment problem. We first give an O(n(q−1)/2))-approximation algorithm for the Koopmans--Beckman version of the problem, improving upon the result of Barvinok. Then, we introduce a new family of instances satisfying “tensor triangle inequalities” and give a constant factor approximation algorithm for them. We show that many classical optimization problems can be modeled by q-adic assignment problems from this family. Finally, we give several integrality gap examples for the natural LP relaxations of the problem.
In this work, we study the existence and multiplicity of positive solutions for the higher order p-Laplacian boundary value problem with even derivatives