Mixed-integer second-order cone optimization (MISOCO) has become very popular in the last decade. Various aspects of solving these problems in Branch and Conic Cut (BCC) algorithms have been studied in the literature. This study aims to fill a gap and provide a novel way to find feasible solutions early in the BCC algorithm. Such solutions … Read more
Extreme events such as disasters cause partial or total disruption of basic services such as water, energy, communication and transportation. In particular, roads can be damaged or blocked by debris, thereby obstructing access to certain affected areas. Thus, restoration of the damaged roads is necessary to evacuate victims and distribute emergency commodities to relief centers … Read more
Given a graph G and an interdiction budget k, the Maximum Clique Interdiction Problem asks to find a subset of at most k vertices to remove from G so that the size of the maximum clique in the remaining graph is minimized. This problem has applications in many areas, such as crime detection, prevention of … Read more
Recently, iterative reweighted methods have attracted much interest in compressed sensing, since they perform better than unweighted ones in most cases. Currently, weights are chosen heuristically in existing iterative reweighted methods, and nding an optimal weight is an open problem since we do not know the exact support set beforehand. In this paper, we present … Read more
A chance constrained optimization problem involves constraints with random data which can be violated with probability bounded above by a prespecified small risk parameter. Such constraints are used to model reliability requirements in a variety of application areas such as finance, energy, service and manufacturing. Except under very special conditions, chance constrained problems are extremely … Read more
We present a new tool for generating cutting planes for NP-hard combinatorial optimisation problems. It is based on the concept of gadgets — small subproblems that are “glued” together to form hard problems — which we borrow from the literature on computational complexity. Using gadgets, we are able to derive huge (exponentially large) new families … Read more
We consider the problem of characterizing the convex hull of the graph of a bilinear function $f$ on the $n$-dimensional unit cube $[0,1]^n$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose the systematic study of properties of $f$ … Read more
In this paper we introduce a new class of bounds for the maximum -cut problem on undirected edge-weighted simple graphs. The bounds involve eigenvalues of the weighted adjacency matrix together with geometrical parameters. They generalize previous results on the maximum (2-)cut problem and we demonstrate that they can strictly improve over other eigenvalue bounds from … Read more
Experimental design is a classical problem in statistics and has also found new applications in machine learning. In the experimental design problem, the aim is to estimate an unknown vector x in m-dimensions from linear measurements where a Gaussian noise is introduced in each measurement. The goal is to pick k out of the given … Read more
We exactly solve the NP-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit … Read more