linear programming
linear programming A technique in optimization, pioneered by George B. Dantzig, that is widely used in economic, military, and businessmanagement decisions. It deals with the problem of finding nonnegative values of the variables x_{1}, x_{2},…, x_{n} that satisfy the constraints a_{i}_{1}x_{1} + a_{i}_{2}x_{2} + … + a_{in}x_{n} = b_{i}, i = 1,2,…,m
and minimize the linear form c_{1}x_{1} + c_{2}x_{2} + … + c_{n}x_{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, an algorithm that terminates after a finite number of steps. It starts at a basic feasible solution and moves through the set of such solutions in such a manner that the value of the linear form is nonincreasing. Very large problems occur in practice involving sparse matrices. Recent work has shown that iterative infinite algorithms are sometimes faster, notably Kamarkar's method.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"linear programming." A Dictionary of Computing. . Encyclopedia.com. 15 Jul. 2018 <http://www.encyclopedia.com>.
"linear programming." A Dictionary of Computing. . Encyclopedia.com. (July 15, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/linearprogramming
"linear programming." A Dictionary of Computing. . Retrieved July 15, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/linearprogramming
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
linear programming
linear programming, solution of a mathematical problem concerning maximum and minimum values of a firstdegree (linear) algebraic expression, with variables subject to certain stated conditions (restraints). For example, the problem might be to find the minimum value of the expression x+y subject to the restraints x≥0, y≥0, 2x+y≥12, 5x+8y≥74, and x+6y≥24. The solution was set forth by the Russian mathematician L. V. Kantorovich in 1939 and was developed independently by the American George B. Dantzig, whose first work on the subject appeared in 1947. A faster, but more complex technique, that is suitable for problems with hundreds or thousands of variables, was developed by Bell Laboratories mathematician Naranda Karmarkar in 1983. Linear programming is particularly important in military and industrial planning.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"linear programming." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 15 Jul. 2018 <http://www.encyclopedia.com>.
"linear programming." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (July 15, 2018). http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/linearprogramming
"linear programming." The Columbia Encyclopedia, 6th ed.. . Retrieved July 15, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/linearprogramming
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.