duality theorem

[dü′al·əd·ē ‚thir·əm]

(mathematics)

A theorem which asserts that for a given n-dimensional space, the (n-p) dimensional homology group is isomorphic to a p-dimensional cohomology group for each p = 0, …, n, provided certain conditions are met.

Let G be either a compact group or a discrete group, let X be its character group, and let G′ be the character group of X ; then there is an isomorphism of G onto G′ so that the groups G and G′ may be identified.

If either of two dual linear-programming problems has a solution, then so does the other.

References in periodicals archive

Our idea is that we first show the metric D is identical with the first Wasserstein metric on P(K) thanks to the duality theorem of Kantorovich-Rubinstein [KR58] (see also Villani's book [V09, Particular Case 5.16]), and then use several definitions for weak contractions which are equivalent to Browder's definition.

Drawing inspiration from Brouwer's work and Poincare's results, in 1922 Alexander formulated his own duality theorem, attaining to the contextual properties of mathematical objects through the analysis of their internal structure (Lautman, 2011).

The surface and the abyss/Rethinking topology

Terai Alexander duality theorem and Stanley-Reisner rings Surikaisekikenkyusho Kokyu- ruko(1999) no.

SOME PROPERTIES OF GLUED GRAPHS AT COMPLETE CLONE IN THE VIEW OF ALGEBRAIC COMBINATORICS

Because [Q.sub.1] [??] 0, the convex set S has an interior point and objective function [[xi].sup.T] [Q.sub.1][xi] + [([q.sub.1] + x).sup.T] [xi] + [r.sub.1] in the left-hand side of (10) is bounded below on S, and from the conic duality theorem, we know that (10) can be transformed into the following problem:

Distributionally robust return-risk optimization models and their applications

Both model (5) and its dual problem are feasible, so by the duality theorem of linear programming they have bounded optimal solutions.

A linear one-model approach for evaluating environmental issues in data envelopment analysis

By the weak duality theorem, ((u,v), [bar.[tau]], [bar.[lambda]], [bar.v]) is an efficient solution of (FD2).

Duality for non smooth multiobjective fractional programming under generalized V-p-invexity

Calderon's remarkable duality theorem [3, Section 12.1 p.

Complex interpolation of compact operators mapping into lattice couples/Vorepaaridesse kujutavate kompaktsete operaatorite kompleksne interpolatsioon

Invoking the Duality Theorem of Linear Programming [22], we arrive at

On economical set representations of graphs

Chapters discuss duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure, calculus of vector- and matrix-valued functions, matrix inequalities, kinematics and dynamics, convexity, the duality theorem, normed liner spaces, linear mappings between normed linear spaces, positive matrices, and solutions of systems of linear equations.

Linear algebra and its applications, 2d ed

Keywords: Evolution equation, Gross Laplacian, potential function, white noise analysis, generalized functions, convolution operator, Laplace transform, duality theorem.

Evolution equation associated with the power of the Gross Laplacian

Teo: A converse duality theorem on higher-order dual models in nondifferentiable mathematical programming, Optim.

Optimality conditions and duality in minmax fractional programming, Part III: second-order parametric duality models