Related papers: Recursive McCormick Linearization of Multilinear P…
In this paper, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex hull representation. Based on the solution of the PPR, we also present a MILP…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
This paper introduces a novel compact mixed integer linear programming (MILP) formulation and a discretization discovery-based solution approach for the Vehicle Routing Problem with Time Windows (VRPTW). We aim to solve the optimization…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…
Recursive McCormick relaxations have been among the most popular convexification techniques for binary polynomial optimization problems. It is well-understood that both the quality and the size of these relaxations depend on the recursive…
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…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in…
The day-ahead electricity market clearing with nonconvex order types can be formulated as a mixed-integer linear program (MILP), but its LP relaxation may provide weak bounds, and exact solutions can become computationally intractable in…
Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…