Nonsmooth exclusion test for finding all solutions of nonlinear equations

DOI10.1007/s10543-010-0280-6zbMath1225.65055OpenAlexW2021085916MaRDI QIDQ616162

Sumit K. Garg

Publication date: 7 January 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.701.8634

zbMATH Keywords

algorithmglobal optimizationbranch-and-bound algorithmconvergencenumerical examplesinterval analysisKrawczyk operatorsystems of nonlinear equationsNewton methodsconvex relaxationinclusionGauss-Seidelinterval Newton-type methodsMcCormick's non-smooth convex relaxationnon-convex problemquasi-Newton type methods

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Nonconvex programming, global optimization (90C26) Numerical computation of solutions to systems of equations (65H10) Methods of quasi-Newton type (90C53) General methods in interval analysis (65G40)

Related Items (3)

Topographical global initialization for finding all solutions of nonlinear systems with constraints ⋮ Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations ⋮ An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator

Uses Software

• INTBIS
• INTOPT_90
• minpack
• PNEW
• libMC

Cites Work

• Bounding solutions of systems of equations using interval analysis
• A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
• Rigorous global search: continuous problems
• Globally convergent variable metric method for convex nonsmooth unconstrained minimization
• Finding all solutions of nonlinearly constrained systems of equations
• Preconditioners for the Interval Gauss–Seidel Method
• McCormick-Based Relaxations of Algorithms
• Abstract Generalized Bisection and a Cost Bound
• Testing Unconstrained Optimization Software
• A Simple Test for Accuracy of Approximate Solutions to Nonlinear (or Linear) Systems
• Interval Methods for Systems of Equations
• Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
• A Test for Existence of Solutions to Nonlinear Systems
• Algorithm 681: INTBIS, a portable interval Newton/bisection package
• Survey of Bundle Methods for Nonsmooth Optimization
• Complete search in continuous global optimization and constraint satisfaction
• Algorithm 811: NDA
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• Unnamed Item
• Unnamed Item
• Unnamed Item

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