Sentence examples for primal function from inspiring English sources

To solve (8) with LOD, (8) is firstly modified by introducing an additional variable, then the primal function (8) reads.

From assumptions (1) and (2), the primal function is concave and the dual function is convex in and for a fixed.

Interestingly, the function p j in (13) has already been studied in the convex literature and it is known as the primal function ([15], Sec. 5.4.4).

It is known that with the dual-based subgradient algorithm using constant step size, the primal function sequence calculated from the running average primal values { x ̂ ( t ) = 1 t ∑ k = 1 t x ( k ), t = 1, 2, … } converges to an optimal value (of P 3 τ ) within an error ([18], Sec. 1.2).

We recall here two main results related to the primal function: (i) p j defines a convex function over the set P j defined as P j = { y j | p j ( y j ) < ∞ } and (ii) the optimal value of the dual variable associated to the constraint h j (x j ) ≤ y j and with opposite sign, say − λ j ∗ ( y j ), is a subgradient of p j at y j.

After degradation, effluxors mediate the release of nutrients to the cytoplasm for reuse [6], a key step in autophagy's primal function as a response to nutrient deprivation.

The template for animal documentaries these days is well established: Go to the ends of the Earth to follow cute, photogenic mammals as they organize their days and lives around the primal functions of eating, mating and nurturing their young.

The parvulins appear to have primal functions, presumably retained from the bacterial lineages within which this PPIase family is the predominant group [ 6, 111], to which they are now largely restrained, whilst the cyclophilins appear to have gained functions at varying stages during fungal evolution.

We denote the optimal primal objective function value by, and the objective function value computed at iteration by.

The difference is called the duality gap of iteration, and it upper bounds the distance from the so far best found primal objective function value to the supremum of the primal objective function.

So, we first investigate the primal objective function and approximate it with a series of convex ones.