We study a predisaster relief network design problem with uncertain demands. The aim is to determine the prepositioning and reallocation of relief supplies. Motivated by the call of the International Federation of Red Cross and Red Crescent Societies (IFRC) to leave no one behind, we consider three important practical aspects of humanitarian operations: shortages, equity, … Read more
Given the measurement matrix $A$ and the observation signal $y$, the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system $y=Ax+z$, where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector. Zhou and Yu \cite{Zhou and Yu 2019} recently proposed a novel … Read more
In this paper, we present a polynomial-time barrier algorithm for solving multi-stage stochastic convex semidefinite optimization based on the Lagrangian dual method which relaxes the nonanticipativity constraints. We show that the barrier Lagrangian dual functions for our setting form self-concordant families with respect to barrier parameters. We also use the barrier function method to improve … Read more
The aim of this paper is to formulate several questions related to distributionally robust Stochastic Optimal Control modeling. As an example, the distributionally robust counterpart of the classical inventory model is discussed in details. Finite and infinite horizon stationary settings are considered. Article Download View Distributionally Robust Modeling of Optimal Control
In this study, we develop a limited memory nonconvex Quasi-Newton (QN) method, tailored to deep learning (DL) applications. Since the stochastic nature of (sampled) function information in minibatch processing can affect the performance of QN methods, three strategies are utilized to overcome this issue. These involve a novel progressive trust-region radius update (suitable for stochastic … Read more
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from slow runtimes, due to weak linear programming (LP) relaxations. In this paper, we first propose a … Read more
Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current flow approximation of the power flow equations in the UC-level and the generator commitments obtained are sent as input to the OPF-level. However, such an … Read more
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are … Read more
This paper discusses chance constrained optimization problems where the constraints are linear to the random variables but nonlinear to the decision variables. For the individual nonlinear chance constraint, we derive tractable reformulation under finite Gaussian mixture distributions and design tight approximation under the generalized hyperbolic distribution. For the joint nonlinear chance constraint, we study several … Read more
Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about … Read more