Related papers: Scalable Mixed-Integer Optimization with Neural Co…
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…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Mixed Integer programs (MIPs) are typically solved by the Branch-and-Bound algorithm. Recently, Learning to imitate fast approximations of the expert strong branching heuristic has gained attention due to its success in reducing the running…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep…
The presented work addresses two-stage stochastic programs (2SPs), a broadly applicable model to capture optimization problems subject to uncertain parameters with adjustable decision variables. In case the adjustable or second-stage…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…
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…
We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse…
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer…
We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of…
Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…
Mixed-integer linear programming (MILP), a widely used modeling framework for combinatorial optimization, are central to many scientific and engineering applications, yet remains computationally challenging at scale. Recent advances in deep…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…
A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time…