Assume that a linear random-effects model (LRM) $\by = \bX \bbe + \bve = \bX\bbe+ \bve$ with $\bbe = \bA \bal + \bga$ is transformed as $\bT\by = \bT\bX\bbe + \bT\bve = \bT\bX\bA \bal + \bT\bX\bga + \bT\bve$ by pre-multiplying a given matrix $\bT$. Estimations/predictions of the unknown parameters under the two models are not … Read more
This article presents a new investigation to the linear mixed model $\by = \bX \bbe + \bZ\bga + \bve$ with fixed effect $\bX\bbe$ and random effect $\bZ\bga$ under a general assumption via some novel algebraic tools in matrix theory, and reveals a variety of deep and profound properties hidden behind the linear mixed model. We … Read more
We present three new approximate versions of alternating direction method of multipliers (ADMM), all of which require only knowledge of subgradients of the subproblem objectives, rather than bounds on the distance to the exact subproblem solution. One version, which applies only to certain common special cases, is based on combining the operator-splitting analysis of the … Read more
Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity … Read more
Many aspects of the classical price-setting newsvendor problem have been studied in the literature and most of the results pertain to the case where the price-demand relationship and demand distribution are explicitly provided. However, in practice, one needs to model and estimate these from historical sales data. Furthermore, many other drivers besides price must be … Read more
We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin’s extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour’s decomposition theorem … Read more
This work is devoted to the study of a proximal decomposition algorithm for solving convex symmetric cone optimization with separable structures. The algorithm considered is based on the decomposition method proposed by Chen and Teboulle (1994), and the proximal generalized distance defined by Auslender and Teboulle (2006). Under suitable assumptions, first a class of proximal … Read more
In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-constraint … Read more
Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In … Read more
We study a daily mine planning problem where, given a set of blocks we wish to mine, our task is to generate a mining sequence for the excavators such that blending resource constraints are met at various stages of the sequence. Such time-oriented resource constraints are not traditionally handled well by automated planners. On the … Read more