Related papers: Integer Programming and m-irreducibility of numeri…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
We show that the number of numerical semigroups with multiplicity three, four or five and fixed genus is increasing as a function in the genus. To this end we use the Kunz polytope for these multiplicities. Counting numerical semigroups…
In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written as an intersection of numerical semigroups properly…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation generated considerable interest, motivating efforts to design efficient…
The $k$-Maximum Dispersion Problem with Cardinality Constraints ($k$-MDCC) asks for a partition of a given item set with pairwise dissimilarities into $k$ cardinality-constrained groups such that the minimum pairwise intra-group…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
The distribution network restoration problem is by nature a mixed integer and non-linear optimization problem due to the switching decisions and Optimal Power Flow (OPF) constraints, respectively. The link between these two parts involves…
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A…
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
The partition of a problem into smaller sub-problems satisfying certain properties is often a key ingredient in the design of divide-and-conquer algorithms. For questions related to location, the partition problem can be modeled, in…
The joint optimization of the integer matrix $\mathbf{A}$ and the power scaling matrix $\mathbf{D}$ is central to achieving the capacity-approaching performance of Integer-Forcing (IF) precoding. This problem, however, is known to be…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex…