New computer methods for global optimization
New computer methods for global optimization
Global optimization of problems with polynomial functions in one variable
Recent advances in global optimization
Numerical methods for global optimization
Recent advances in global optimization
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
A New Inclusion Function for Optimization: Kite&mdashlThe One Dimensional Case
Journal of Global Optimization
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In this paper we define multisections of intervals that yield sharp lower bounds in branch-and-bound type methods for interval global optimization. A so called 'generalized kite', defined for differentiable univariate functions, is built simultaneously with linear boundary forms and suitably chosen centered forms. Proofs for existence and uniqueness of optimal cuts are given. The method described may be used either as an accelerating device or in a global optimization algorithm with an efficient pruning effect. A more general principle for decomposition of boxes is suggested.