convex duality

convex duality
мат. выпуклая двойственность

Большой англо-русский и русско-английский словарь. 2001.

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  • Convex optimization — Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space X together with a convex, real valued function defined on a convex subset of X, the problem is to find …   Wikipedia

  • Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

  • Duality gap — In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If d * is the optimal dual value and p * is the optimal primal value then the duality gap is equal to p * − d * . This value …   Wikipedia

  • Convex conjugate — In mathematics, convex conjugation is a generalization of the Legendre transformation. It is also known as Legendre–Fenchel transformation or Fenchel transformation (after Adrien Marie Legendre and Werner Fenchel). Contents 1 Definition 2… …   Wikipedia

  • Convex cone — In linear algebra, a convex cone is a subset of a vector space over an ordered field that is closed under linear combinations with positive coefficients. A convex cone (light blue). Inside of it, the light red convex cone consists of all points… …   Wikipedia

  • Mathematical economics — Economics …   Wikipedia

  • Dual problem — In constrained optimization, it is often possible to convert the primal problem (i.e. the original form of the optimization problem) to a dual form, which is termed a dual problem. Usually dual problem refers to the Lagrangian dual problem but… …   Wikipedia

  • Linear programming — (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships.… …   Wikipedia

  • Claude Lemaréchal — is a French applied mathematician. In mathematical optimization, Claude Lemaréchal is known for his work in numerical methods for nonlinear optimization, especially for problems with nondifferentiable kinks. Lemaréchal and Phil. Wolfe pioneered… …   Wikipedia

  • Dual polyhedron — The dual of a cube is an octahedron, shown here with vertices at the cube face centers …   Wikipedia

  • Oriented matroid — theory allows a combinatorial approach to the max flow min cut theorem. A network with the value of flow equal to the capacity of an s t cut An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of… …   Wikipedia


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