Sentence examples for by replacing the convex from inspiring English sources

Finally, problem (P) generalizes the one investigated in [21], and the proposed algorithm can be directly applied to solve the problem in [19] by replacing the convex feasibility with the linear one.

It is known that one can extend his result from a single strict pseudocontraction to a finite family of strict pseudocontractions by replacing the convex combination of these mappings in the iteration under suitable conditions.

The claim that the function s ↦ Φ i ( x, y ; p, g, f s ) is log-convex on I is an immediate consequence of Theorem 3.7 and Remark 3.5, and (24) can be obtained by replacing the convex function f with the convex function f ( z ) = log Φ i ( x, y ; p, g, f z ) for z = r, s, t in (21), where r, s, t ∈ I such that r < s < t.

For instance, to estimate the labor supply of married women on 1985 French data, Bourguignon and Magnac (1990) use the Hausman technique and eliminate minor non-convexities by replacing the budget set by its convex envelope.

We can extend this definition to a locally convex space by replacing the norm with a family of seminorms.

The core idea of CCP is to decompose the optimization of a non-convex problem into an iterative procedure, and in each iteration, the problem is modified as a convex one by replacing the concave part in the objective function with a Taylor's approximation.

We show that the relaxed formulation is obtained by replacing the set of characteristic functions by its convex envelope.

Fortunately, a relaxation of the above problem was shown to produce very accurate approximations, by replacing the rank constraint by the tractable nuclear norm, which represents the convex envelope of the rank [6].

Hence, any complete RNA structure or RNA RNA interaction prediction dynamic programming algorithm can be transformed into a Newton polytope algorithm by replacing the energy with the corresponding feature vector, summation with the Minkowski sum and minimization with the convex hull of union.

By replacing the cemented-doublet of the traditional eyepiece with a diffractive-refractive element (a plano-convex lens with the plane surface as the diffractive surface) an improved eyepiece is obtained.

If we consider strictly convex Banach spaces, as in [18], we can obtain the same kind of conclusions by replacing the condition (b) by a more suitable one.