We consider an aerial survey operation in which a fleet of unmanned aerial vehicles (UAVs) is required to visit several locations and then land in one of the available landing sites while optimising some performance criteria, subject to operational constraints and flight dynamics. We aim to minimise the maximum flight time of the UAVs. To … Read more
\(\) A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative … Read more
A new decoder for the SIF test problems of the \cutest\ collection is described, which produces problem files allowing the computation of values and derivatives of the objective function and constraints of most \cutest\ problems directly within “native” Matlab, Python or Julia, without any additional installation or interfacing with MEX files or Fortran programs. When … Read more
Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent … Read more
We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop’s user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented … Read more
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial optimization. In this formulation, we assume that the variables are partitioned into a fixed number of sets, and … Read more
\(\) We consider sequential testing problems that involve a system of \(n\) stochastic components, each of which is either working or faulty with independent probability. The overall state of the system is a function of the state of its individual components, and the goal is to determine the system state by testing its components at … Read more
Facial reduction is a pre-processing method aimed at reformulating a problem to ensure strict feasibility. The importance of constructing a robust model is widely recognized in the literature, and facial reduction has emerged an attractive approach for achieving robustness. In this note, we outline a facial reduction algorithm for a standard spectrahedra, the intersection of … Read more