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INTRODUCTIONCONSISTENCYConsistency in Discrete SearchLine-Search AlgorithmsConsistency in Linear and Convex ProgrammingRENORMALISATIONTowards a Dynamical System RepresentationRenormalisation in Line-Search AlgorithmsRenormalisation of Ellipsoid AlgorithmsRenormalisation in the Steepest Descent AlgorithmSquare AlgorithmRATES OF CONVERGENCEErgodic Rates of ConvergenceCharacteristics of Average PerformancesCharacteristics of Worst-Case PerformancesCounting CharacteristicOne-Dimensional Piecewise Linear MappingsLINE-SEARCH ALGORITHMSFirst-Order Line SearchContinued Fraction Expansion and the Gauss MapGolden-Section AlgorithmErgodically Optimal Second-Order Line Search AlgorithmSymmetric AlgorithmsMidpoint and Window AlgorithmsAlgorithms Based on Section Invariant NumbersComparisons of GS, GS4, GS40 and Window AlgorithmsELLIPSOID ALGORITHMSVolume-Optimal Outer and Inner EllipsoidsErgodic Behaviour of the Outer-Ellisoid AlgorithmSTEEPEST DESCENT ALGORITHMAttraction to a Two-Dimensional PlaneStability of AttractorsRate of ConvergenceSteepest Descent with RelaxationAppendixEntropiesErgodic TheorySection-Invariant NumbersReferencesAuthor IndexSubject Index