Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. By definition, strong duality holds if and only if the duality gap is equal to 0. This is opposed to weak duality (the primal problem has optimal value smaller than or equal to the dual problem, in other words the duality gap is greater than or equal to zero).
are equal. By definition, strongduality holds if and only if the duality gap is equal to 0. This is opposed to weak duality (the primal problem has optimal...
belong to a larger class of duality theorems in optimization. The strongduality theorem is one of the cases in which the duality gap (the gap between the...
sometimes referred to as duality gap. When the value of the primal and dual SDPs are equal, the SDP is said to satisfy the strongduality property. Unlike linear...
areas of mathematics, the strongdual space of a topological vector space (TVS) X {\displaystyle X} is the continuous dual space X ′ {\displaystyle X^{\prime...
In applied mathematics, weak duality is a concept in optimization which states that the duality gap is always greater than or equal to 0. This means that...
The duality gap is zero if and only if strongduality holds. Otherwise the gap is strictly positive and weak duality holds. In general given two dual pairs...
is the traditional definition of Fenchel duality. Radu Ioan Boţ; Gert Wanka; Sorin-Mihai Grad (2009). Duality in Vector Optimization. Springer. ISBN 978-3-642-02885-4...
the dual cone of C {\displaystyle C\ } . Whilst weak duality holds in conic linear programming, strongduality does not necessarily hold. The dual of...
}[g(y)]\\f(x)+g(y)\leq c(x,y)\end{cases}}} and the strongduality still holds. This is the Kantorovich duality theorem. Cédric Villani recounts the following...
of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems of computational...
if y ≤ x. The new order is commonly called dual order of ≤, and is mostly denoted by ≥. Therefore, duality plays an important role in order theory and...
Two theories related by a duality need not be string theories. For example, Montonen–Olive duality is an example of an S-duality relationship between quantum...
duality. If the two sides are equal to each other, then the problem is said to satisfy strongduality. There are many conditions for strongduality to...
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...
at any feasible solution. The strongduality theorem states that if the primal has an optimal solution, x*, then the dual also has an optimal solution...
In mathematics, a dual system, dual pair or a duality over a field K {\displaystyle \mathbb {K} } is a triple ( X , Y , b ) {\displaystyle (X,Y,b)} consisting...
by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded...
they are both DF-spaces. Then, denoting strongdual spaces with a subscripted b {\displaystyle b} : The strongdual of N ⊗ ^ π Y {\displaystyle N{\widehat...
repeating theme in duality theory, which is that any definition for a pairing ( X , Y , b ) {\displaystyle (X,Y,b)} has a corresponding dual definition for...
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