Related papers: Extended Formulations via Decision Diagrams

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data…

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that…

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…

The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…

Mathematical programming formulations of influence diagrams can bridge the gap between representing and solving decision problems. However, they suffer from both modeling and computational limitations. Aiming to address modeling…

The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Influence diagrams are widely employed to represent multi-stage decision problems in which each decision is a choice from a discrete set of alternatives, uncertain chance events have discrete outcomes, and prior decisions may influence the…

We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

This paper studies the problem of finding an $(1+\epsilon)$-approximate solution to positive semidefinite programs. These are semidefinite programs in which all matrices in the constraints and objective are positive semidefinite and all…

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…