Branch-and-bound methods for solving systems of Lipschitzian equations and inequalities

DOI10.1007/BF00939776zbMath0621.90073OpenAlexW1984516801MaRDI QIDQ1090614

Nguyen Van Thoai, Reiner Horst

Publication date: 1988

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00939776

zbMATH Keywords

fixed pointsbranch-and-boundsystems of inequalitiesmultiextremal global optimizationsystems of Lipschitzian equations

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10)

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The cost of not knowing enough: mixed-integer optimization with implicit Lipschitz nonlinearities, A method for solving d.c. programming problems. Application to fuel mixture nonconvex optimization problem, Utility function programs and optimization over the efficient set in multiple-objective decision making, Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and d.c. optimization problems, New LP bound in multivariate Lipschitz optimization: Theory and applications, A successive linear relaxation method for MINLPs with multivariate Lipschitz continuous nonlinearities, An application of Lipschitzian global optimization to product design, Calculation of bounds on variables satisfying nonlinear inequality constraints, Solving nonlinear equation systems via global partition and search: Some experimental results, A decomposition method for MINLPs with Lipschitz continuous nonlinearities, Concave minimization via conical partitions and polyhedral outer approximation

Cites Work

• Extended univariate algorithms for \(n\)-dimensional global optimization
• On the convergence of global methods in multiextremal optimization
• Deterministic global optimization with partition sets whose feasibility is not known: Application to concave minimization, reserve convex constraints, DC-programming and Lipschitzian optimization
• The Approximation of Fixed Points of a Continuous Mapping