Related papers: A Lagrange decomposition based Branch and Bound al…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…
Cloud computing is a new paradigm where data and services of Information Technology are provided via the Internet by using remote servers. It represents a new way of delivering computing resources allowing access to the network on demand.…
Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…
The Optimal Power Flow (OPF) problem is central to the reliable and efficient operation of power systems, yet its non-convex nature poses significant challenges for finding globally optimal solutions. While convex relaxation techniques such…
Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…
Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
We propose exact solution approaches for a lateral transhipment problem which, given a pre-specified sequence of customers, seeks an optimal inventory redistribution plan considering travel costs and profits dependent on inventory levels.…
We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the gripper's kinematics feasibility into consideration to ensure…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…
With the skyrocketing costs of GPUs and their virtual instances in the cloud, there is a significant desire to use CPUs for large language model (LLM) inference. KV cache update, often implemented as allocation, copying, and in-place…
We introduce the problem of optimal congestion control in cache networks, whereby \emph{both} rate allocations and content placements are optimized \emph{jointly}. We formulate this as a maximization problem with non-convex constraints, and…