An Upper Bound on the Number of Measurements Required by the Contour Tangent Optimization Technique

An upper bound for the number of measurements required by the contour tangent optimization technique [1], [3] to give an ϵ approximation to the maximum is determined. The bound is applicable to n-dimensional quasiconcave functions and requires an estimate of the modulus of continuity δ near the maximum. For large even n and domain on the unit interval, the number of contour tangent measurements required is less than 2.18n (𝓃 ln n - ln δ - 0.22). If each contour tangent is approximated by n + 1 explicit measurements of the objective, then an upper bound on the number of function evaluations is n + 1 times the above. The bound derived shows that the contour tangent technique is far superior to dichotomous search [3], the next best direct search elimination technique.