Results 1 
8 of
8
A Comparison of Complete Global Optimization Solvers
"... Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables. ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.
GloptLab, a configurable framework for the rigorous global solution of quadratic constraint satisfaction problems
"... solution of quadratic constraint satisfaction problems ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
solution of quadratic constraint satisfaction problems
Constraint propagation on quadratic constraints
, 2008
"... This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear en ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is taken to ensure that all methods correctly account for rounding errors in the computations.
Rigorous Affine Lower Bound Functions for Multivariate Polynomials and Their Use in Global Optimisation
"... This paper addresses the problem of finding tight affine lower bound functions for multivariate polynomials, which may be employed when global optimisation problems involving polynomials are solved with a branch and bound method. These bound functions are constructed by using the expansion of the gi ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
This paper addresses the problem of finding tight affine lower bound functions for multivariate polynomials, which may be employed when global optimisation problems involving polynomials are solved with a branch and bound method. These bound functions are constructed by using the expansion of the given polynomial into Bernstein polynomials. The coefficients of this expansion over a given box yield a control point structure whose convex hull contains the graph of the given polynomial over the box. We introduce a new method for computing tight affine lower bound functions based on these control points, using a linear least squares approximation of the entire control point structure. This is demonstrated to have superior performance to previous methods based on a linear interpolation of certain specially chosen control points. The problem of how to obtain a verified affine lower bound function in the presence of uncertainty and rounding errors is also considered. Numerical results with error bounds for a series of randomlygenerated polynomials are given. Key words: Constrained global optimisation, relaxation, affine bound functions, Bernstein polynomials, linear least squares 1
Interval Propagation on Directed Acyclic Graphs Interval Propagation and Search on Directed Acyclic Graphs for Numerical Constraint Solving
"... The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed by Schichl and Neumaier [2005]. For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose directed edges are ..."
Abstract
 Add to MetaCart
The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed by Schichl and Neumaier [2005]. For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose directed edges are computational flows. Compared to treebased representations [Benhamou et al. 1999], DAGs offer the essential advantage of more accurately handling the influence of subexpressions shared by several constraints on the overall system during propagation. In this paper we show how interval constraint propagation and search on DAGs can be made practical and efficient by: 1) flexibly choosing the nodes on which propagations must be performed, and 2) working with partial subgraphs of the initial DAG rather than with the entire graph. We propose a new interval constraint propagation technique which exploits the influence of subexpressions on all the constraints together rather than on individual constraints. We then show how the new propagation technique can be integrated into branchandprune search to solve numerical constraint satisfaction problems. This algorithm is able to outperform its obvious contenders, as shown by the experiments. 1 1.
GloptLab – Quickstart Guide
, 2008
"... This is the Quickstart Guide to GloptLab. It guides the reader through the first steps in the use of GloptLab, a testing and development platform for solving quadratic constraint satisfaction problems, written in Matlab. First we describe how to install GloptLab. In Section 2 we give a stepbystep i ..."
Abstract
 Add to MetaCart
This is the Quickstart Guide to GloptLab. It guides the reader through the first steps in the use of GloptLab, a testing and development platform for solving quadratic constraint satisfaction problems, written in Matlab. First we describe how to install GloptLab. In Section 2 we give a stepbystep instruction making the user become familiar with GloptLab quickly. Additionally to this guide the user may find helpful tooltips given in the graphical user interface (GUI) of GloptLab. For further details – in particular information on how to extend GloptLab easily by adding user defined methods – see [1].