We describe Pyomo, an open-source tool for modeling optimization applications in Python. Pyomo can be used to define abstract problems, create concrete problem instances, and solve these instances with standard solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages like AMPL and GAMS. Pyomo leverages the capabilities of the Coopr software, … Read more
Good scaling is an essential requirement for the good behavior of many numerical algorithms. In particular, for problems involving multivariate polynomials, a change of scale in one or more variable may have drastic effects on the robustness of subsequent calculations. This paper surveys scaling algorithms for systems of polynomials from the literature, and discusses some … Read more
Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to … Read more
A method for generating a sequence of intensity-modulated radiation therapy step-and-shoot plans with increasing number of segments is presented. The objectives are to generate high-quality plans with few, large and regular segments, and to make the planning process more intuitive. The proposed method combines segment generation with direct step-and-shoot optimization, where leaf positions and segment … Read more
Abstract: After developing necessary background theory, the original primal and dual are specified, and the invariant primal and dual LP’s are defined. Pairs of linear mappings are defined which establish an effectively one-to-one correspondences between solutions to the original and invariant problems. The invariant problems are recast as a fixed-point problem and precise solution conditions … Read more
We present a general metaheuristic for joint chance-constrained stochastic programs with discretely distributed parameters. We give a reformulation of the problem that allows us to define a finite solution space. We then formulate a novel neighborhood for the problem and give methods for efficiently searching this neighborhood for solutions that are likely to be improving. … Read more
We provide information on the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design that can be accessed at http://sndlib.zib.de. In version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network planning problem instances. In this paper, we … Read more
This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American option pricing. The paper proposes an improvement of a method described by Kocvara and Zowe that combines … Read more
Sheet metal forming is a significant manufacturing process for producing a large variety of automotive parts and aerospace parts as well as consumer products. Deep drawing is a compression-tension forming process involving wide spectrum of operations and flow conditions. The result of the process depends on the large number of parameters and their interdependence. With … Read more
We present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer programming (MIP) model and a linear programming (LP) model are used to find an optimal … Read more