We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more
Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot … Read more
Interior methods provide an effective approach for the treatment of inequality constraints in nonlinearly constrained optimization. A new primal-dual interior method is proposed based on minimizing a sequence of shifted primal-dual penalty-barrier functions. Certain global convergence properties are established. In particular, it is shown that every limit point is either an infeasible stationary point, or … Read more
Influence maximization problems aim to identify key players in (social) networks and are typically motivated from viral marketing. In this work, we introduce and study the Generalized Least Cost Influence Problem (GLCIP) that generalizes many previously considered problem variants and allows to overcome some of their limitations. A formulation that is based on the concept … Read more
In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov introduced the power cone, together with a 4-self-concordant barrier for it. In his PhD thesis, Chares found an improved 3-self-concordant barrier for the power cone. In addition, he introduced the generalized power cone, and conjectured a nearly optimal self-concordant barrier for … Read more
In this paper, we focus on solving matrix completion problem arising from applications in the fields of information theory, statistics, engineering, etc. However, the matrix completion problem involves nonconvex rank constraints which make this type of problem difficult to handle. Traditional approaches use a nuclear norm surrogate to replace the rank constraints. The relaxed model … Read more
Total dual integrality is a powerful and unifying concept in polyhedral combinatorics and integer programming that enables the refinement of geometric min-max relations given by linear programming Strong Duality into combinatorial min-max theorems. The definition of total dual integrality (TDI) revolves around the existence of optimal dual solutions that are integral, and thus naturally applies … Read more
In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more
We introduce a framework for quasi-Newton forward–backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal +/- rank-r symmetric positive definite matrices. This special type of metric allows for a highly efficient evaluation of the proximal mapping. The key to this efficiency is a general proximal calculus in the new metric. By using … Read more
We consider a continuous time variant of the Inventory Routing Problem in which the maximum quantity that can delivered at a customer depends on the customer’s storage capacity and product inventory at the time of the delivery. We investigate critical components of a dynamic discretization discovery algorithm and demonstrate in an extensive computational study that … Read more