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Global optimization over unbounded domains. (English) Zbl 0725.90086
The paper presents a technique to solve the global optimization problem for a continuous function without the assumption that a parallelepiped containing the solution is a priori known. The technique is based on the branch-and-bound method and on infinite-interval arithmetic. Bounds of the global optimum are generated and one or several boxes of prescribed size that include all global minimizers are produced. It can be detected when the function has no global optimum at all and further, whether or not it is bounded. The sharpness of these detections is limited by the finite number representation of computers.

MSC:
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
90-08 Computational methods for problems pertaining to operations research and mathematical programming
65K10 Numerical optimization and variational techniques
65G30 Interval and finite arithmetic
90C26 Nonconvex programming, global optimization
90C31 Sensitivity, stability, parametric optimization
90C32 Fractional programming
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