Related papers: Solving MIPs via Scaling-based Augmentation
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Geometric scaling, introduced by Schulz and Weismantel in 2002, solves the integer optimization problem $\max \{c\mathord{\cdot}x: x \in P \cap \mathbb Z^n\}$ by means of primal augmentations, where $P \subset \mathbb R^n$ is a polytope. We…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a…
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…
Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…
We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…
The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however,…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
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…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints…
We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times.…
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…
Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a new optimization-via-compilation strategy to scalably solve a certain class of such problems. In…
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…
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…
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…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…