Constraint propagation on quadratic constraints

Domes, Ferenc; Neumaier, Arnold

doi:10.1007/s10601-009-9076-1

Cited by 28 publications

(25 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are several novel branching strategies within Couenne [27]. -GloptLAB [42,43,44,45] GloptLAB is a Matlab-based framework for solving quadratic constraint satisfaction problems [42]. The GloptLAB bounding and scaling strategies are particularly interesting [43,44,45].…”

Section: Literature Reviewmentioning

confidence: 99%

“…-GloptLAB [42,43,44,45] GloptLAB is a Matlab-based framework for solving quadratic constraint satisfaction problems [42]. The GloptLAB bounding and scaling strategies are particularly interesting [43,44,45]. -LindoGLOBAL [63,87] Like αBB, BARON, and Couenne, LindoGLOBAL addresses generic MINLP to global optimality with specific routines for quadratic components.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Variable bounding algorithms relevant to this work include: interval arithmetic bounds tightening [6,7,15,18,27,127,128], optimality-based bounds tightening [89,133], reduced cost bounds tightening [117,118], and quadratic equation constraint satisfaction [44,45,77].…”

Section: Literature Reviewmentioning

confidence: 99%

See 2 more Smart Citations

GloMIQO: Global mixed-integer quadratic optimizer

2012

View full text Add to dashboard Cite

This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2,

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

GloMIQO: Global mixed-integer quadratic optimizer

2012

View full text Add to dashboard Cite

show abstract

“…This can be generalized for arbitrary quadratic functions, see [3,4]. With these new expressions and the exponential node (denoted here by exp(v, c) = e cv ), y m (x,t) is represented as 35) with c = −t/2.…”

Section: Reformulation Of the Problemmentioning

confidence: 99%

Verified Global Optimization for Estimating the Parameters of Nonlinear Models

Kieffer

Markót

Schichl

et al. 2011

Modeling, Design, and Simulation of Systems With Uncertainties

View full text Add to dashboard Cite

Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools instrumental for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available.

show abstract

“…Since interval linear systems are embedded into the interval union framework, any algorithm that relies on the rigorous solution of interval linear systems can benefit from the methods discussed in this paper. For example, constraint propagation methods [5] and the interval Newton operator [20,21] can be significantly improved with the use of interval union techniques. Moreover, interval union linear systems of equations can be used to define an interval union branch and bound framework for rigorous global optimization.…”

Section: Introductionmentioning

confidence: 99%

Using interval unions to solve linear systems of equations with uncertainties

et al. 2017

Self Cite

View full text Add to dashboard Cite

An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss-Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss-Jordan preconditioners. The Gauss-Jordan preconditioner is used in a mixed strategy to improve the quality and efficiency of the algorithm. Numerical experiments on interval linear systems generated at random show the capabilities of our approach.

show abstract

Constraint propagation on quadratic constraints

Cited by 28 publications

References 29 publications

GloMIQO: Global mixed-integer quadratic optimizer

GloMIQO: Global mixed-integer quadratic optimizer

Verified Global Optimization for Estimating the Parameters of Nonlinear Models

Using interval unions to solve linear systems of equations with uncertainties

Contact Info

Product

Resources

About