This article deals with the calmness of a solution map of a Cournot Oligopoly Game with nonsmooth cost functions. The fact that the cost functions are not supposed to be differentiable allows for considering cases where some firms have diferent units of production, which have diferent marginal costs. In order to obtain results about the … Read more
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for such problems. However, quantifying the uncertainty associated with the underlying training algorithm is not well-studied in the non-convex setting. In order to address this short-coming, in this work, … Read more
We propose a new universal framework for multi-stage decision making under limited information availability. It is developed as part of a larger research project which aims at providing analytical methods to compare and evaluate different models and algorithms for multi-stage decision making. In our setting, we have an open time horizon and limited information about … Read more
Influence maximization (IM) is a challenging combinatorial optimization problem on (social) networks given a diffusion model and limited choice for initial seed nodes. In a recent paper an integer programming formalization of IM using the so-called deterministic linear threshold diffusion model was proposed. In fact, it is a special 0-1 linear program in which the … Read more
Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single- and multi-stage problems involving real-valued and/or binary decisions, and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a … Read more
We consider a single machine scheduling problem to minimize the completion time variance. This roblem is known to be NP-hard. We prove that if $p_{n-1} = p_{n-2$, then there is an optimal solution of the form $(n,n-2,n-3,…,n-4,n-1)$. A new lower bound are proposed for solving the problem. The test on more than 4000 instances shows … Read more
In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature … Read more
Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more
This work proposes a progressive manifold identification approach for distributed optimization with sound theoretical justifications to greatly reduce both the rounds of communication and the bytes communicated per round for partly-smooth regularized problems such as the $\ell_1$- and group-LASSO-regularized ones. Our two-stage method first uses an inexact proximal quasi-Newton method to iteratively identify a sequence … Read more
The field of Statistical Disclosure Control aims at reducing the risk of re-identification of an individual when disseminating data, and it is one of the main concerns of national statistical agencies. Operations Research (OR) techniques were widely used in the past for the protection of tabular data, but not for microdata (i.e., files of individuals … Read more