相关论文: Ranking Constraint Relaxations for Mixed Integer P…

We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…

We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…

In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…

Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…

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…

This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by…

We study logit-based multi-purchase choice models and develop an exact solution methodology for the resulting assortment optimization problems, which we show are NP-hard to approximate. We introduce a hypergraph representation that captures…

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of…

The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…

Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output label space. These constraints interact with the learned models to filter infeasible…

Multi-label classification (MLC) is an ML task of predictive modeling in which a data instance can simultaneously belong to multiple classes. MLC is increasingly gaining interest in different application domains such as text mining,…

Hyperparameters in machine learning (ML) have received a fair amount of attention, and hyperparameter tuning has come to be regarded as an important step in the ML pipeline. But just how useful is said tuning? While smaller-scale…

We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…

Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…

In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using Mixed-Integer Programming (MIP). Our MIP model balances the optimization of prediction…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

We address the Interval Data Min-Max Regret 0-1 Integer Linear Programming problem (MMR-ILP), a variant of the 0-1 Integer Linear Programming problem where the objective function coefficients are uncertain. We solve MMR-ILP using a…

This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside…