x > y yields True if x is determined to be greater than y. x_1 > x_2 > x_3 yields True if the x_i form a strictly decreasing sequence.

x <= y or x <= y yields True if x is determined to be less than or equal to y. x_1 <= x_2 <= x_3 yields True if the x TraditionalForm\`i form a nondecreasing sequence.

x < y yields True if x is determined to be less than y. x_1 < x_2 < x_3 yields True if the x_i form a strictly increasing sequence.

Linear programming problems are optimization problems where the objective function and constraints are all linear. Mathematica has a collection of algorithms for solving ...

FindArgMin[f, x] gives the position x_min of a local minimum of f.FindArgMin[f, {x, x_0}] gives the position x_min of a local minimum of f, found by a search starting from ...

FindMinValue[f, x] gives the value at a local minimum of f.FindMinValue[f, {x, x_0}] gives the value at a local minimum of f, found by a search starting from the point x = ...

NMaximize[f, x] maximizes f numerically with respect to x.NMaximize[f, {x, y, ...}] maximizes f numerically with respect to x, y, .... NMaximize[{f, cons}, {x, y, ...}] ...

Monte Carlo methods use randomly generated numbers or events to simulate random processes and estimate complicated results. For example, they are used to model financial ...

Mathematica has a collection of commands that do unconstrained optimization (FindMinimum and FindMaximum) and solve nonlinear equations (FindRoot) and nonlinear fitting ...

FindShortestTour[{e_1, e_2, ...}] attempts to find an ordering of the e_i that minimizes the total distance on a tour that visits all the e_i once.