Sentence examples for primal vector from inspiring English sources

The basic idea of the weighted-sum method is to introduce a so-called weight vector [38] that is positive in the dual cone (K^={mathbb {R}}_ +^{2}) and then to transform the primal vector optimization problem into a scalar optimization problem.

In their models, the ("primal") vector space represented quantitites while the "dual" vector space represented prices.

This family usually applies machine learning-based approaches such as linear discriminant analysis (LDA) [8, 9], primal rank support vector machine (RankSVM) [10], and multi-view discriminant analysis (MvDA) [11].

With the "block vector view", the primal optimization problem for GRMT SVR (10) can be reformulated as follows.

Suppose that the vector-valued functions f and g in the primal problem (CLFP) can be parameterized as the vector-valued functions (mathbf{f}_{epsilon}) and (mathbf{g}_{epsilon}) for (epsilon>0) in which (mathbf{f}_{epsilon}) and (mathbf{g}_{epsilon}) are assumed to be continuous functions on ([0,T]) and (mathbf{g}_{epsilon}(t geqmathbf{0}) for all (tin[0,T]).

We assume for simplicity that in the vector u ∼ the essential primal DOF are listed first, i.e. (30) u ∼ = (u ∼ d, u ∼ f, u ∼ R ) T = (u ∼ d, u ∼ f, u ∼ R (1 ), …, u ∼ R (N ) ) T and K ∼ = K ∼ dd K ∼ df K ∼ dR K ∼ fd K ∼ ff K ∼ fR K ∼ Rd K ∼ Rf K ∼ RR, f ∼ = f ∼ d f ∼ f f ∼ R, B ∼ = B ∼ d B ∼ f B ∼ R. Let g ∼ d be the vector whose entries are the values of g D at the essential primal DOF.

This paper gives a primal-dual derivation of the Least Squares Support Vector Machine (LS-SVM) using Instrumental Variables (IVs), denoted simply as the Primal-dual Instrumental Variable Estimator.

Our asymptotic runtime compares favourably with conventional ('primal') methods, because primal methods search for full-length parameter vectors in a space that grows exponentially with the number of parameters.

A not so simple matter is how to recover an optimal primal pair (x∗,p∗) given an optimal dual vector Λ∗.

Since we apply the cutting plane algorithm to solve the dual problem, the primal recovery scheme to obtain the optimal rate vector r ⋆ and the optimal time shares τ i ⋆ is fairly simple.

It is based on kernel spectral clustering (KSC), a model designed in the Least Squares Support Vector Machines (LS-SVMs) framework, with primal-dual setting.