##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
Convexity preservation
as a function of (the value of ) is convex and piecewise linear. Initially, , a V-shape centered at .
Adding keeps convexity. The constraint "" truncates the function on the left, preserving only the non-decreasing part. The minimum of is at the largest breakpoint less than or equal to the current choice. A max-heap tracks these breakpoints.
