Related papers: Progressively Strengthening and Tuning MIP Solvers…
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We…
This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…
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…
Mixed-integer model predictive control (MI-MPC) can be a powerful tool for modeling hybrid control systems. In case of a linear-quadratic objective in combination with linear or piecewise-linear system dynamics and inequality constraints,…
Machine learning frameworks adopt iterative optimizers to train neural networks. Conventional eager execution separates the updating of trainable parameters from forward and backward computations. However, this approach introduces…
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…
Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training…
This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a…
In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all…
The EURO/ROADEF 2010 Challenge aimed to schedule the maintenance and refueling operations of French nuclear power plants, ranking the approaches in competition for the quality of primal solutions. This paper justifies the high quality of…
In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…
Decision trees are a popular machine learning model which are traditionally trained by heuristic methods. Massive improvements in computing power and optimisation techniques has led to renewed interest in learning globally optimal decision…
Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms such as the pooling problem. These methods convert the original nonconvex optimization problems into mixed-integer linear…
To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem.…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing…
The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed…
This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called…
We present a new method for large language models to solve compositional tasks. Although they have shown strong performance on traditional language understanding tasks, large language models struggle to solve compositional tasks, where the…
Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has…