Optimal centered forms

DOI10.1007/BF01934696zbMath0641.65043MaRDI QIDQ1100850

Eckart Baumann

Publication date: 1988

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

global optimizationinterval arithmeticone-sided isotonicityoptimal centered form

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30)

Related Items (28)

A second-order pruning step for verified global optimization ⋮ Bernstein form is inclusion monotone ⋮ Solving minimax problems by interval methods ⋮ On interval branch-and-bound for additively separable functions with common variables ⋮ Empirical convergence speed of inclusion functions for facility location problems ⋮ Robust analysis and design of control systems using interval arithmetic ⋮ Interval methods for global optimization ⋮ A class of componentwise Krawczyk-Moore type iteration methods ⋮ A Branch-and-Prune Method for Global Optimization ⋮ Global optimization of disjunctive programs ⋮ Robot workspace approximation with modified bicentered Krawczyk method ⋮ Bound constrained interval global optimization in the COCONUT environment ⋮ Multi-dimensional pruning from the Baumann point in an interval global optimization algorithm ⋮ Global optimization of generalized semi-infinite programs using disjunctive programming ⋮ Continuous minimax optimization using modal intervals ⋮ Theoretical rate of convergence for interval inclusion functions ⋮ Convergent upper bounds in global minimization with nonlinear equality constraints ⋮ Global solution of semi-infinite programs ⋮ Comparison between Baumann and admissible simplex forms in interval analysis ⋮ An extension of the \(\alpha\mathrm{BB}\)-type underestimation to linear parametric Hessian matrices ⋮ On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic ⋮ Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint ⋮ Interval expansion method for nonlinear equation in several variables ⋮ New results on verified global optimization ⋮ Optimal centers in branch-and-prune algorithms for univariate global optimization ⋮ Empirical investigation of the convergence speed of inclusion functions in a global otimization context ⋮ A new inclusion function for optimization: kite -- the one-dimensional case ⋮ Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints

Cites Work

• Unnamed Item
• Mean value forms in interval analysis
• Die zentrische Form in der Intervallarithmetik, ihre quadratische Konvergenz und ihre Inklusionsisotonie
• Interval Slopes for Rational Functions and Associated Centered Forms
• Quadratic convergence in interval arithmetic, part I

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