https://slow-is-smooth.io/tags/lagrangian-relaxation/Recent content in Lagrangian Relaxation on Shai AsherHugoen-gbTue, 27 Oct 2026 12:00:00 +0200https://slow-is-smooth.io/blog/the-cleaning-robot-puzzle-a-price-on-every-move/Tue, 27 Oct 2026 12:00:00 +0200https://slow-is-smooth.io/blog/the-cleaning-robot-puzzle-a-price-on-every-move/<p><em>With a battery of five moves, Part 2&rsquo;s robot collects 14 units of dirt, and the best route collects 16. Charge the robot 3¼ units of dirt for every move it makes, and it can be proved that no route collects more than 17. A drawing shows why no price, however well chosen, can prove 16.</em></p>