INDEX 657 for conic problems, 433 motivation, 262 quadratic function on sphere, 268 without multipliers, 264 second welfare theorem, 386, 389 self-concordant barrier method, 335 self-concordant barriers, 339 semidefinite programming, 340, 418 separation of convex sets, 253 setting sun, illusion of, 65 shareholders versus stakeholders, 106, 158 short position, 378 simplex method, 284 idea of, 284 sine, behind the button, 13 slackness, 237 Slater point, 210 smoothness, role in optimization, 45 Snellius, law of, 39 soap films, 107 social welfare, 61, 193 solid convex cone, 420 producer theory, basic problem, 192 product, row vector and column vec- tor, 509 production and inventory, 462 profit maximization, not optimal, 105 proof multiplier rule, 180 Pythagorean theorem n-dimensional, 88 quadratic function, 93 rank, 516 rank matrix, 507 RAS method, 370 ray, 419 real numbers, 519 reasonable descent, proof of neces- sary conditions, 134 refined tangent space theorem, 189 relation, two high school formulas, 27 relativity of time, 432 remainder term, 92 risk minimization investment, 251