Interval Analysis: Unconstrained and Constrained Optimization

INTERVAL ANALYSIS: UNCON-STRAINED AND CONSTRAINED OPTIMIZATION Introduction. Interval algorithms for constrained and un-constrained optimization are based on adaptive, exhaustive search of the domain. Their overall structure is virtually identical to Lipschitz optimization as in [4], since interval evaluations of an objective function φ over an interval vector x correspond to estimation of the range of φ over x with Lipschitz constants. However, there are additional opportunities for acceleration of the process with interval algorithms, and use of outwardly rounded interval arithmetic gives the computations the rigor of a mathematical proof. The interval algorithms are both complicated and accelerated by the presence of constraints, as is explained below. See Interval analysis: Introduction, interval numbers, and basic properties of interval arithmetic for background on interval computations. See [5], [2] or [3] for further details of concepts in this article. The basic problem is