This works addresses the resolution of penalized least-squares problems using the proximal gradient algorithm (PGA). It is known that PGA can be accelerated by preconditioning strategies. However, typical effective choices of preconditioners may correspond to intricate matrices that are not easily inverted, and lead to an increased complexity in the computation of the proximity step. … Read more
Range-extended electric vehicles combine the higher efficiency and environmental benefits of battery-powered electric motors with the longer mileage and autonomy of conventional internal combustion engines. This combination is particularly advantageous for time-constrained delivery routing in dense urban areas, where battery recharging along routes can be too time-consuming to economically justify the use of all-electric vehicles. … Read more
The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation using cubics algorithm inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the … Read more
In this paper, we introduce the Targeted Multiobjective Dijkstra Algorithm (T-MDA), a label setting algorithm for the One-to-One Multiobjective Shortest Path (MOSP) Problem. The T-MDA is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*-like techniques. The resulting speedup is comparable to the speedup that the original A* algorithm achieves … Read more
We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lagrangian optimality gap with a … Read more
A novel approach based on a specialized interior-point method (IPM) is presented for solving large-scale stochastic multistage continuous optimization problems, which represent the uncertainty in strategic multistage and operational two-stage scenario trees, the latter being rooted at the strategic nodes. This new solution approach considers a split-variable formulation of the strategic and operational structures, for … Read more
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs Jacobi-type proximal updates of the augmented Lagrangian function, requiring only local solutions of separable block nonlinear programming (NLP) problems. We provide a cheap and explicitly computable Lyapunov function that allows … Read more
We introduce the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decision and congestion cost effect into the problem and allowing dynamic routing for origin-destination pairs. Connecting strategic and operational level decisions, … Read more
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. … Read more
In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of … Read more