Globally Optimized Finite Packings of Arbitrary Size Spheres in R^d

This work discusses the following general packing problem-class: given a finite collection of d-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in R^d that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to this general problem-type, except for very small … Read more

Combining Progressive Hedging with a Frank-Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual … Read more

A predictor-corrector path-following algorithm for dual-degenerate parametric optimization problems

Most path-following algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions, in particular, the linear independence of the constraint gradients at the solutions, which implies a unique multiplier solution for every nonlinear program. In this paper we propose and prove … Read more

On the NP-Completeness of the Multi-Period Minimum Spanning Tree Problem

In this note, we consider the Multi-period Minimum Spanning Tree Problem (MMST), a variant of the well known Minimum Spanning Tree Problem (MST), that consists in the fol- lowing. Given a connected and undirected graph G and a finite discrete time horizon, one has to schedule the moment in time edges are added to a … Read more

Linearized Robust Counterparts of Two-stage Robust Optimization Problem with Applications in Operations Management

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that … Read more

Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

Let $\Gamma:=\{x\in \R^n\, |\, q(x)\in\Theta\},$ where $q: \R^n\rightarrow\R^m$ is a twice continuously differentiable mapping, and $\Theta$ is a nonempty polyhedral convex set in $\R^m.$ In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping $N_\Gamma:\R^n\rightrightarrows\R^n,$ $x\mapsto N_\Gamma(x),$ under the condition that $M_q(x):=q(x)-\Theta$ is metrically subregular at … Read more

A new algebraic analysis to linear mixed models

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

Bid Markup Decision and Resource Allocation for Cost Estimation in Competitive Bidding

To receive a project contract through competitive bidding, contractors submit a bid price determined by putting a markup on the estimated project cost. Since a bid is inevitably affected by an inaccurate cost estimate, sufficient resources should be allocated to cost estimation. This paper develops a novel optimization model for determining the bid markup and … Read more

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation … Read more

Semi-Smooth Second-order Type Methods for Composite Convex Programs

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as forward-backward splitting (FBS) and Douglas-Rachford splitting (DRS), actually define a possibly semi-smooth and monotone fixed-point mapping; ii) The optimal solutions … Read more