Sentence examples for in a dual form from inspiring English sources

This may in turn be formulated in a dual form.

Forward-backward splitting algorithms were proposed by Lions and Mercier [12], by Passty [13], and, in a dual form for convex programming, by Han and Lou [14].

The logic of espousing humanism,15 a feature of anticommunist films at the time, manifested in a dual form in anticommunist films.

This constrained optimization problem can be expressed equivalently in a dual form by searching a solution under the form θ = ∑ i = 1 N α i y i x i.

Forward-backward splitting algorithms, which have recently received much attention to many mathematicians, were proposed by Lions and Mercier [4], by Passty [5], and, in a dual form for convex programming, by Han and Lou [6].

Forward-backward splitting algorithms, which have recently received much attention from many mathematicians, were proposed by Lions and Mercier [3], by Passty [4], and, in a dual form for convex programming, by Han and Lou [5].

Earlier forms of the epsilon calculus (such as that presented in (Hilbert 1923)) use a dual form of the epsilon operator, in which εx A returns a value falsifying A x).

Note that (1.7) is the -Busemann-Petty centroid inequality (1.2), (1.8) is the dual form of -Busemann-Petty centroin inequaliTheoremheorem B, (1.9) is a "dual" form of -Petty projection inequality, and (1.10) is the -Petty projection inequality (1.1).

Thus cognition, in its perceptual aspect, has a dual form: subjectively, it discloses a bare consciousness that merely attends to the flow of sensations; objectively, it corresponds to each specific domain of empirical awareness: visual objects to visual awareness, sounds to auditory awareness, etc.

Ours is a dual form of government; in every State there are two Governments -- the State and the United States; each State has all governmental powers save such as the people, by the Constitution, have conferred upon the United States, denied to the States, or reserved to themselves.

Rewriting the above problem in the dual form, the kernel-trick, specifying a function giving the inner-product of two vectors in a higher dimensional vector space, can then be applied and an optimal separating hyperplane can be found in this new vector space.