Related papers: Provably Data-driven Lagrangian Relaxation for Mix…
We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$…
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…
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 investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
The augmented Lagrangian method (ALM) is classic for canonical convex programming problems with linear constraints, and it finds many applications in various scientific computing areas. A major advantage of the ALM is that the step for…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Optimal planning with respect to learned neural network (NN) models in continuous action and state spaces using mixed-integer linear programming (MILP) is a challenging task for branch-and-bound solvers due to the poor linear relaxation of…
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…
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…
Space mission planning and spacecraft design are tightly coupled and need to be considered together for optimal performance; however, this integrated optimization problem results in a large-scale Mixed-Integer Nonlinear Programming (MINLP)…
Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible…