Optimization Models for Differentiating Quality of Service Levels in Probabilistic Network Capacity Design Problems

Categories Network Optimization, Stochastic Programming, Transportation

This paper develops various chance-constrained models for optimizing the probabilistic network design problem (PNDP), where we differentiate the quality of service (QoS) and measure the related network performance under uncertain demand. The upper level problem of PNDP designs continuous/discrete link capacities shared by multi-commodity flows, and the lower level problem differentiates the corresponding QoS for … Read more

Quantitative Characterizations of Regularity Properties of Collections of Sets

Categories Nonsmooth Optimization

Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided. CitationJOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS (2015) 164:41–67ArticleDownload View PDF

On Solving a Hard Quadratic 3-Dimensional Assignment Problem

Categories Branch and Cut Algorithms, Telecommunications Tags , ,

We address the exact solution of a very challenging (and previously unsolved) instance of the quadratic 3-dimensional assignment problem, arising in digital wireless communications. The paper describes the techniques developed to solve this instance to proven optimality, from the choice of an appropriate mixed-integer programming formulation, to cutting planes and symmetry handling. Using these techniques … Read more

Complementarity Formulations of l0-norm Optimization Problems

Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , ,

In a number of application areas, it is desirable to obtain sparse solutions. Minimizing the number of nonzeroes of the solution (its l0-norm) is a difficult nonconvex optimization problem, and is often approximated by the convex problem of minimizing the l1-norm. In contrast, we consider exact formulations as mathematical programs with complementarity constraints and their … Read more

Smooth minimization of nonsmooth functions with parallel coordinate descent methods

Categories Convex Optimization, Parallel Algorithms Tags , , , ,

We study the performance of a family of randomized parallel coordinate descent methods for minimizing the sum of a nonsmooth and separable convex functions. The problem class includes as a special case L1-regularized L1 regression and the minimization of the exponential loss (“AdaBoost problem”). We assume the input data defining the loss function is contained … Read more

A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing

Categories Applications - Science and Engineering, Nonlinear Optimization Tags , ,

We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement matrices, we derive a sufficient condition for convergence of IHT to a fixed point and a necessary condition for the existence … Read more

Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

Categories Production and Logistics, Supply Chain Management, Transportation Tags , , , , ,

We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each belonging to a particular vessel class, between loading and discharging ports, each belonging to a particular region. Our algorithms iteratively solve a MIRP by zooming … Read more

A pseudo-polynomial size formulation for 2-stage two-dimensional knapsack problems

Categories (Mixed) Integer Linear Programming Tags , ,

Two dimensional cutting problems are about obtaining a set of rectangular items from a set of rectangular stock pieces and are of great relevance in industry, whenever a sheet of wood, metal or other material has to be cut. In this paper, we consider the 2-stage two-dimensional knapsack (2TDK) problem which requires finding the maximum … Read more

Primal-dual methods for solving infinite-dimensional games

Categories Convex and Nonsmooth Optimization, Semi-infinite Programming Tags , , ,

In this paper we show that the infinite-dimensional differential games with simple objective functional can be solved in a finite-dimensional dual form in the space of dual multipliers for the constraints related to the end points of the trajectories. The primal solutions can be easily reconstructed by the appropriate dual subgradient schemes. The suggested schemes … Read more

Rounding on the standard simplex: regular grids for global optimization

Categories Constrained Nonlinear Optimization, Global Optimization Theory

Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all $\ell^p$-norms for $p\ge 1$. We show that the minimal $\ell^p$-distance to the regular grid on the standard simplex can exceed one, even for very fine … Read more