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Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…
For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the…
In statistical learning, many problem formulations have been proposed so far, such as multi-class learning, complementarily labeled learning, multi-label learning, multi-task learning, which provide theoretical models for various real-world…
We propose a new disjunctive regularization for mathematical programs with complementarity constraints (MPCC). Its feasible set coincides with that of the Kanzow-Schwartz regularization. However, their functional descriptions differ…
We propose an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures…
The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
Mixed Hamming packings are considered: the maximal cardinality given a minimum codeword Hamming distance of mixed codes is addressed via mixed integer programming models. Adopting the concept of contact graph from classical continuous…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
Compared to legacy wavelength division multiplexing networks, elastic optical networks (EON) have added flexibility to network deployment and management. EONs can include previously available technology, such as signal regeneration and…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…
This paper addresses the single-item single-stocking location stochastic lot sizing problem under the $(s, S) $ policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal $(s, S)$ policy…
Online conformal prediction has demonstrated its capability to construct a prediction set for each incoming data point that covers the true label with a predetermined probability. To cope with potential distribution shift, multi-model…
Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal…
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs…
We consider two covering variants of the network design problem. We are given a set of origin/destination pairs, called O/D pairs, and each such O/D pair is covered if there exists a path in the network from the origin to the destination…
Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…