Related papers: Efficient exact sequential lifting algorithm for b…
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…
Binarization is an extreme network compression approach that provides large computational speedups along with energy and memory savings, albeit at significant accuracy costs. We investigate the question of where to binarize inputs at…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex…
The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential…
Modern electric power systems have witnessed rapidly increasing penetration of renewable energy, storage, electrical vehicles and various demand response resources. The electric infrastructure planning is thus facing more challenges due to…
This paper introduces bucket calculus, a novel mathematical framework that fundamentally transforms the computational complexity landscape of parallel machine scheduling optimization. We address the strongly NP-hard problem…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
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…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this…
Binary Knapsack Problem (BKP) is to select a subset of an element (item) set with the highest value while keeping the total weight within the capacity of the knapsack. This paper presents an integer programming model for a variation of BKP…
Scheduling multiple products with limited resources and varying demands remain a critical challenge for many industries. This work presents mixed integer programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) and other Dynamic…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using Mixed-Integer Programming (MIP). Our MIP model balances the optimization of prediction…
A covering integer program (CIP) is a mathematical program of the form: min {c^T x : Ax >= 1, 0 <= x <= u, x integer}, where A is an m x n matrix, and c and u are n-dimensional vectors, all having non-negative entries. In the online…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…