Related papers: Branch-and-bound for integer D-Optimality with fas…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization…
We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration…
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
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…
In this paper, we present a branch and bound algorithm for extracting approximate solutions to Global Polynomial Optimization (GPO) problems with bounded feasible sets. The algorithm is based on a combination of SOS/Moment relaxations and…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
Local branching is an improvement heuristic, developed within the context of branch-and-bound algorithms for MILPs, which has proved to be very effective in practice. For the binary case, it is based on defining a neighbourhood of the…
Given an undirected graph and a size parameter $k$, the Densest $k$-Subgraph (D$k$S) problem extracts the subgraph on $k$ vertices with the largest number of induced edges. While D$k$S is NP--hard and difficult to approximate, penalty-based…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an…
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…