https://abaj.ai/tags/polytope/Recent content in Polytope on Aayush Bajaj's Augmenting InfrastructureHugoen© 2026 Aayush BajajThu, 09 Jul 2026 21:02:37 +1000https://abaj.ai/wiki/ccs/programming/paradigms/linear/Thu, 09 Jul 2026 21:02:56 +1000https://abaj.ai/wiki/ccs/programming/paradigms/linear/<p>&ldquo;programming&rdquo; here means <em>planning</em>, not coding — the word predates the software sense.<span class="margin-note" data-note="dantzig invented the simplex method in 1947 for air-force logistics planning; kantorovich had the theory in 1939 but the soviets sat on it"> <span class="margin-note-indicator">𐃏</span> </span> a linear program optimises a linear objective over a region carved out by linear inequalities. it is the base camp of mathematical programming: <a href="https://abaj.ai/wiki/ccs/programming/paradigms/quadratic/" >quadratic</a>, <a href="https://abaj.ai/wiki/ccs/programming/paradigms/integer/" >integer</a> and <a href="https://abaj.ai/wiki/ccs/programming/paradigms/non-linear/" >non-linear</a> programming all generalise it in one direction or another, and all of them lean on LP machinery (relaxations, duals, warm starts) to get anything done. clrs devotes chapter 29 to it (Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford, 2009).</p>