https://abaj.ai/tags/relaxation/Recent content in Relaxation on Aayush Bajaj's Augmenting InfrastructureHugoen© 2026 Aayush BajajFri, 10 Jul 2026 08:15:51 +1000https://abaj.ai/wiki/ccs/programming/paradigms/integer/Fri, 10 Jul 2026 01:43:39 +1000https://abaj.ai/wiki/ccs/programming/paradigms/integer/<p>take a <a href="https://abaj.ai/wiki/ccs/programming/paradigms/linear/" >linear program</a> and add one word — <em>integer</em> — and the complexity class jumps from polynomial to NP-hard. that word buys expressive power nothing continuous can match: yes/no decisions, either/or logic, fixed costs, sequencing, assignment. integer programming is the lingua franca of operations research precisely because &ldquo;decide&rdquo; is not a convex verb.<span class="margin-note" data-note="commercial solvers — gurobi, cplex, scip — routinely crack instances with millions of variables, np-hardness notwithstanding. hard in the worst case is not hard on your case"> <span class="margin-note-indicator">𐃏</span> </span> </p>