Algorithm 1: Piecewise-linear Algorithm
Ø The number of is C, let t = C/m.
Ø If , the minimax point is searched from the left , otherwise, from . We only describe the search process of start from the left, and the right is the same. Solving the intersection coordinates of the and , let and , if the corresponding , then terminate the search and is the solution of the subproblem.
Ø If , then solving the intersection coordinates of the straight line with a slope bigger than and the current line .
Ø Here, the number of lines where the slope is larger than is recorded as w, remember , let , and judge whether the abscissa is out of bounds, if , then x = 1 is the solution of the subproblem, otherwise judge whether or not , if , then stop to research, and is the solution of the subproblem, otherwise repeat the step 3, until the minimax point is found.