Related papers: Efficient primal heuristics for mixed-integer line…

The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently…

We posit that we can generate more robust and performant heuristics if we augment approaches using LLMs for heuristic design with tools that explain why heuristics underperform and suggestions about how to fix them. We find even simple…

Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored.…

In multiprocessor systems, one of the main factors of systems' performance is task scheduling. The well the task be distributed among the processors the well be the performance. Again finding the optimal solution of scheduling the tasks…

In imitation learning for planning, parameters of heuristic functions are optimized against a set of solved problem instances. This work revisits the necessary and sufficient conditions of strictly optimally efficient heuristics for forward…

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…

We present the findings of the first NeurIPS competition on unlearning, which sought to stimulate the development of novel algorithms and initiate discussions on formal and robust evaluation methodologies. The competition was highly…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…

Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…

This work focuses on learning optimization problems with quadratical interactions between variables, which go beyond the additive models of traditional linear learning. We investigate more specifically two different methods encountered in…

Ignoring uncertainty in combinatorial optimization leads to suboptimal decisions in practice. Nevertheless, the focus is often on deterministic combinatorial optimization problems, mainly because they are already challenging enough without…

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…

This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…

As machine learning (ML) systems get adopted in more critical areas, it has become increasingly crucial to address the bias that could occur in these systems. Several fairness pre-processing algorithms are available to alleviate implicit…

We introduce Scylla, a primal heuristic for mixed-integer optimization problems. It exploits approximate solves of the Linear Programming relaxations through the matrix-free Primal-Dual Hybrid Gradient algorithm with specialized termination…

Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification,…

Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…

Since the rise of Large Language Models (LLMs) a couple of years ago, researchers in metaheuristics (MHs) have wondered how to use their power in a beneficial way within their algorithms. This paper introduces a novel approach that…

We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…