State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics … Read more
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use r-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such … Read more
In this paper, scalarizing functions defined with the help of the Hiriart-Urruty signed distance are used to characterize set order relations and weak optimal solutions in set optimization studied with Kuroiwa’s set approach and to introduce a new concept of slope for a set-valued map. It turns out that this slope possesses most properties of … Read more
Critical infrastructure systems in cities are becoming increasingly interdependent, therefore exacerbating the impacts of disruptive events through cascading failures, hindered asset repairs and network congestion. Current resilience assessment methods fall short of fully capturing such interdependency effects as they tend to model asset reliability and network flows separately and often rely on static flow assignment … Read more
Two-trust-region subproblem (TTRS), which is the minimization of a general quadratic function over the intersection of two full-dimensional ellipsoids, has been the subject of several recent research. In this paper, to solve TTRS, a hybrid of efficient algorithms for finding global and local-nonglobal minimizers of trust-region subproblem and the alternating direction method of multipliers (ADMM) … Read more
In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov’s smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov’s smoothing techniques and DC programming that involves the $\ell_1-\ell_2$ regularization. ArticleDownload View PDF
The global container shipping network is vital to international trade. Current techniques for its vulnerability assessment are constrained due to the lack of historical disruption data and computational limitations due to typical network sizes. We address these modelling challenges by developing a new framework, composed by game-theoretic attacker-defender model and a cost-based container assignment model … Read more
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and con- tinuous time. The set of all invariant measures is characterized as the feasible set of an infinite-dimensional linear program (LP). The objective functional of this LP is then used to single-out a specific measure … Read more
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuousand discrete-time polynomial systems, under semialgebraic set constraints. First, we address the problem of approximating the density and hence the support of an invariant measure which is absolutely continuous with respect to … Read more
We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive tractable semidefinite programming approximations for instances where the set is defined by affine and quadratic inequalities. We prove that, … Read more