Madelyn Dunham, 86, Senator Barack Obama’s grandmother, died late Sunday evening in Hawaii after battling cancer, which Mr. Obama announced upon arriving here on Monday for a campaign stop on the eve of Election Day. “She has gone home,” Mr. Obama said, his voice tinged with emotion as he briefly spoke of her death at a campaign rally here. “She died peacefully in her sleep with my sister at her side, so there’s great joy instead of tears.” … Mr. Obama broke from the presidential campaign trail late last month to travel to Honolulu to bid his grandmother farewell. He spent part of two days with her, as she lay gravely ill in the small apartment where he lived from age 10 to 18.