{"id":"optimization","domain":"applied","type":"Concept","title":"Optimization","slug":"optimization","url":"/mathematics/applied/optimization/","summary":"Finds the best solution from feasible options. Calculus-based methods, Lagrange multipliers, linear programming, gradient descent. Underlies machine learning.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press."},{"tier":1,"citation":"Nocedal, J. and Wright, S.J. (2006). Numerical Optimization. 2nd ed."},{"tier":2,"citation":"Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press."},{"tier":3,"citation":"Gershenfeld, N. (1999). The Nature of Mathematical Modeling."}],"relationships":[{"type":"uses","target":"derivative","label":"Derivative — critical points, gradients"},{"type":"uses","target":"matrix","label":"Matrix — Hessian, linear programming"},{"type":"related_to","target":"noethers-theorem","label":"Noether's Theorem — Principle of Least Action"},{"type":"applied_in","target":"game-theory","label":"Game Theory"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.1"}