Figure 2.

Illustration of 2-dimension coordinate binary search algorithm. This is a visualization of a bivariate concave function with its contours. The maximum point is (1, 2). The arrowed line segments show the procedures of coordinate binary search algorithm when optimizing this function. The initial search point is (2.5, 0.5) and search direction is parallel with y axis. In this step of optimization, we fixed x = 2.5 and the bivariate function degenerated in to a univariate function with respect to only y. Since the original function is concave, this degenerated function is also concave and can be optimized by binary search algorithm. After we get the optimum of this degenerated function, the next step of coordinate binary search algorithm is to fix y to the current optimum’s projection on y axis and search in the direction parallel with x axis. These procedures are iterated and the optimum of this function will be finally reached.