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  2. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

  3. Linear bottleneck assignment problem - Wikipedia

    en.wikipedia.org/wiki/Linear_bottleneck...

    The formal definition of the bottleneck assignment problem is Given two sets, A and T, together with a weight function C : A × T → R.Find a bijection f : A → T such that the cost function:

  4. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Since the following is valid:

  5. LP-type problem - Wikipedia

    en.wikipedia.org/wiki/LP-type_problem

    Some geometric optimization problems may be expressed as LP-type problems in which the number of elements in the LP-type formulation is significantly greater than the number of input data values for the optimization problem. As an example, consider a collection of n points in the plane, each

  6. Farkas' lemma - Wikipedia

    en.wikipedia.org/wiki/Farkas'_lemma

    Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively, mathematical programming). It is used amongst other things in the proof of the Karush–Kuhn–Tucker theorem in nonlinear programming . [ 2 ]

  7. Basic solution (linear programming) - Wikipedia

    en.wikipedia.org/wiki/Basic_solution_(Linear...

    In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...

  8. Benders decomposition - Wikipedia

    en.wikipedia.org/wiki/Benders_decomposition

    Benders decomposition (or Benders' decomposition) is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure. This block structure often occurs in applications such as stochastic programming as the uncertainty is usually represented with scenarios.

  9. Fundamental theorem of linear programming - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners.