Linear Programming Definition/Meaning:

A technique in optimization, pioneered by George B. Dantzig, that is widely used in economic, military, and business-management decisions. It deals with the problem of finding nonnegative values of the variables x₁, x₂, . . . x_n that satisfy the constraints

a_i1x₁ + a_i2x_{2 +}. . . . . . +a_inx_{n =} b_i,

i = 1,2,...m

and minimize the linear form

c₁x_{1 +} c₁x_{2 + .. . . . +} c_nx_n

Maximizing problems and problems with inequality constraints or unrestricted variables can be converted to this form. An optimum solution (if any exist) is known to be a basic feasible solution, which is one that satisfies the constraints and has at most m positive x_i values.

Computationally such problems are solved by the simplex method, which starts at a basic feasible solution and searches the set of such solutions in such a manner that the value of the linear form is nonincreasing. An important recent advance is the algorithm developed by N.Z. Shor and L. G. Khachian. In theory this is significantly faster than the simplex method but it is as yet uncertain whether this can be realized in practice.

Near by Terms: LIFO or lifo (Last in first out) Light Pen Likelihood       Linear Algebraic Equations (simultaneous equations) Linear Array Linear-Bounded Automaton (LBA) Linear Channel Linear Codes Linear Logic Linearly Addressed Memory (two-dimensional (2-D) memory) Linear Programming Linear Recurrence LIFO or lifo (Last in first out) Light Pen Likelihood       Linear Algebraic Equations (simultaneous equations) Linear Array Linear-Bounded Automaton (LBA) Linear Channel Linear Codes Linear Logic Linearly Addressed Memory (two-dimensional (2-D) memory) Linear Programming Linear Recurrence Linear Structure (totally ordered structure) Line Discipline Line Finder Line Printer Line Protocol (line discipline) Line Switching Link Link Editor (linkage editor) Linked List (chained list) Link Encryption Link Loader Link Testing LISP List List Head List Processing List Sorting Literal Linear Structure (totally ordered structure) Line Discipline Line Finder Line Printer Line Protocol (line discipline) Line Switching Link Link Editor (linkage editor) Linked List (chained list) Link Encryption Link Loader Link Testing LISP List List Head List Processing List Sorting Literal