An efficient and safe framework for solving optimization problems

DOI10.1016/j.cam.2005.08.037zbMath1108.65065OpenAlexW1988446106MaRDI QIDQ861905

Claude Michel, Michel Rueher, Yahia Lebbah

Publication date: 2 February 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.037

zbMATH Keywords

algorithmsglobal optimizationconvergenceconsistencynumerical examplesinterval arithmeticconstraint programmingQuadOptsafe linear relaxations

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Interval and finite arithmetic (65G30) Packaged methods for numerical algorithms (65Y15)

Related Items (7)

Global optimization with spline constraints: a new branch-and-bound method based on B-splines ⋮ Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects ⋮ Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems ⋮ Global optimization of mixed-integer nonlinear (polynomial) programming problems: The Bernstein polynomial approach ⋮ Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm ⋮ Constraint propagation using dominance in interval branch \& bound for nonlinear biobjective optimization ⋮ \texttt{lsmear}: a variable selection strategy for interval branch and bound solvers

Uses Software

• INTOPT_90

Cites Work

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• A comparative performance evaluation of 27 nonlinear programming codes
• The convergence rate of the sandwich algorithm for approximating convex functions
• Rigorous global search: continuous problems
• Safe bounds in linear and mixed-integer linear programming
• Safe and tight linear estimators for global optimization
• Convexification and global optimization in continuous and mixed-integer nonlinear programming. Theory, algorithms, software, and applications
• Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization
• Complete search in continuous global optimization and constraint satisfaction
• Validated Linear Relaxations and Preprocessing: Some Experiments
• Efficient and Safe Global Constraints for Handling Numerical Constraint Systems

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