Sentence examples for by replacing a quadratic from inspiring English sources

By replacing a quadratic term ∥ y − x ∗ ∥ 2 in the subproblem (1.1) by the Bregman distance function, Nguyen et al. in [15] proposed the interior proximal extragradient method for solving EP ( f, C ), where f is pseudomonotone and C only is a polyhedron convex set.

by replacing a T with a G.

In this paper, we propose the cubic body wave equation as an extension to Barrett's formulation by replacing the quadratic amplitude expression by a cubic spline polynomial.

The ridge regression [39] problem in Equation 2 can be transformed into the SVR optimization problem by replacing the quadratic loss with the ε-insensitive linear loss, l ε (f(x i ) − y i ) = max{0,f(x i ) − y i } which is shown in Figure 1B: min w, b ∥ w ∥ 2 + C ∑ i = 1 m ξ + ξ ∗ subject to: f ( x i ) - y i ≤ ε + ξ y i - f ( x i ) ≤ ε + ξ ∗ ξ, ξ ∗ ≥ 0 (3).

This is achieved by replacing the purely quadratic cost function employed within the MPC optimization by a mixed linear-quadratic cost function.

The Hasofer Lind reliability index is determined by the Rackwitz Fiessler algorithm in which the performance function is replaced by a quadratic response surface in order to reduce computational cost and gain accuracy.

The basic idea in bent-cable regression is that the kink in the broken-stick model is replaced by a quadratic bend with midpoint τ and half-width δ.

Firstly, by replacing the constant amplitude by a quadratic amplitude wave and secondly, by provisioning that α can act as both an amplitude growth and dampening factor.

The first author treating the stability of the quadratic equation was Skof [27] by proving that if f is a mapping from a normed space X into a Banach space Y satisfying ||f(x + y) + f(x -y)- 2f(x) - 2f y)|| ≤ ε for some ε > 0, then there is a unique quadratic mapping g: X → Y such that f ( x ) - g ( x ) ≤ ε 2. Cholewa [28] extended the Skof's theorem by replacing X by an abelian group G.

This corresponds to replacing

We next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region.