While the security proof method for quantum key distribution, QKD, based on the numerical key rate calculation problem, is powerful in principle, the practicality of the method is limited by computational resources and the efficiency of the underlying algorithm for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model … Read more
In this paper we consider minimization of a difference-of-convex (DC) function with and without linear constraints. We first study a smooth approximation of a generic DC function, termed difference-of-Moreau-envelopes (DME) smoothing, where both components of the DC function are replaced by their respective Moreau envelopes. The resulting smooth approximation is shown to be Lipschitz differentiable, … Read more
During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, … Read more
Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterisation of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: we discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight … Read more
We consider a stochastic version of the 0–1 Knapsack Problem in which, in addition to profit and weight, each item is associated with a probability of exploding and destroying all the contents of the knapsack. The objective is to maximize the expected profit of the selected items. The resulting problem, denoted as 0–1 Time-Bomb Knapsack … Read more
Peer-to-peer logistics platforms coordinate independent drivers to fulfill requests for last mile delivery and ridesharing. To balance demand-side performance with driver autonomy, a new methodology is created to provide drivers with a small but personalized menu of requests to choose from. This creates a Stackelberg game, in which the platform leads by deciding what menu … Read more
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in performing an iterative search for the shift akin to solving the secular equation in trust-region methods. Such search requires computing the Cholesky factorization of … Read more
We develop a trust-region method for minimizing the sum of a smooth term f and a nonsmooth term h, both of which can be nonconvex. Each iteration of our method minimizes apossibly nonconvex model of f+h in a trust region. The model coincides with f+h in value and subdifferential at the center. We establish global … Read more
Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we … Read more
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more