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- Linear_programming abstract "Linear programming (LP, or linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.Linear programs are problems that can be expressed in canonical form:where x represents the vector of variables (to be determined), c and b are vectors of (known) coefficients, A is a (known) matrix of coefficients, and is the matrix transpose. The expression to be maximized or minimized is called the objective function (cTx in this case). The inequalities Ax ≤ b and x ≥ 0 are the constraints which specify a convex polytope over which the objective function is to be optimized. In this context, two vectors are comparable when they have the same dimensions. If every entry in the first is less-than or equal-to the corresponding entry in the second then we can say the first vector is less-than or equal-to the second vector.Linear programming can be applied to various fields of study. It is used in business and economics, but can also be utilized for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.".
- Linear_programming thumbnail Linear_optimization_in_a_2-dimensional_polytope.svg?width=300.
- Linear_programming wikiPageExternalLink LinearProgramming.
- Linear_programming wikiPageExternalLink glossary.computing.society.informs.org.
- Linear_programming wikiPageExternalLink LinearProgrammingFAQ.htm.
- Linear_programming wikiPageExternalLink LP.
- Linear_programming wikiPageExternalLink Problems.
- Linear_programming wikiPageExternalLink lp.html.
- Linear_programming wikiPageExternalLink bench.html.
- Linear_programming wikiPageExternalLink ormpug_optmodel_sect005.htm.
- Linear_programming wikiPageExternalLink dut-twi-94-73.ps.gz.
- Linear_programming wikiPageExternalLink LP-survey.html.
- Linear_programming wikiPageExternalLink oxford.ps.
- Linear_programming wikiPageExternalLink LPbook.
- Linear_programming wikiPageExternalLink dantzig.html.
- Linear_programming wikiPageExternalLink zimpl.zib.de.
- Linear_programming wikiPageID "43730".
- Linear_programming wikiPageRevisionID "604210252".
- Linear_programming hasPhotoCollection Linear_programming.
- Linear_programming subject Category:Convex_optimization.
- Linear_programming subject Category:Geometric_algorithms.
- Linear_programming subject Category:Linear_programming.
- Linear_programming subject Category:Mathematical_and_quantitative_methods_(economics).
- Linear_programming subject Category:Operations_research.
- Linear_programming subject Category:P-complete_problems.
- Linear_programming comment "Linear programming (LP, or linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.".
- Linear_programming label "Lineair programmeren".
- Linear_programming label "Linear programming".
- Linear_programming label "Lineare Optimierung".
- Linear_programming label "Optimisation linéaire".
- Linear_programming label "Programación lineal".
- Linear_programming label "Programação linear".
- Linear_programming label "Programmazione lineare".
- Linear_programming label "Programowanie liniowe".
- Linear_programming label "Линейное программирование".
- Linear_programming label "برمجة خطية".
- Linear_programming label "線型計画法".
- Linear_programming label "线性规划".
- Linear_programming sameAs Lineární_programování.
- Linear_programming sameAs Lineare_Optimierung.
- Linear_programming sameAs Programación_lineal.
- Linear_programming sameAs Programazio_lineal.
- Linear_programming sameAs Optimisation_linéaire.
- Linear_programming sameAs Pemrograman_linier.
- Linear_programming sameAs Programmazione_lineare.
- Linear_programming sameAs 線型計画法.
- Linear_programming sameAs 선형_계획법.
- Linear_programming sameAs Lineair_programmeren.
- Linear_programming sameAs Programowanie_liniowe.
- Linear_programming sameAs Programação_linear.
- Linear_programming sameAs m.0byrz.
- Linear_programming sameAs Q202843.
- Linear_programming sameAs Q202843.
- Linear_programming wasDerivedFrom Linear_programming?oldid=604210252.
- Linear_programming depiction Linear_optimization_in_a_2-dimensional_polytope.svg.
- Linear_programming isPrimaryTopicOf Linear_programming.
