Sentence examples for by first minimizing the from inspiring English sources

Therefore, P ∗ can be found by first minimizing the Lagrangian (mathcal {L}_{mathrm {{PM}}}) in (13) to evaluate the dual objective function d in (20) and then maximizing d over all non-negative values of μ and λ.

The algorithm described in [ 70] has a linear time complexity, and, given a polytomous gene tree G, binary species tree S, and their mapping α, searches for a binarization G* of G by first minimizing the total sum of duplications and then the total sum of losses in the obtained set of binarizations.

Second, minimize the scheduling delay.

First, by minimizing the restructuring of the SKB data structure, most of existing code can be reused without major code development.

As in the complete situation, if we want to use (2.6) and (2.8), it is a must to estimate α first, by minimizing the sum of square errors min_{alpha} sum_{i=1}^{n} bigl[Y_{i}^{ast}-V_{i}^{T}breve{ beta}_{n}-breve {g}_{n}bigl(Z_{i}^{T} alphabigr bigr]^{2}, (2.9) say (breve{alpha}_{n}).

Second, by minimizing the obtained SER upper bound, we formulate and compare three schemes to optimize the relay placement and power allocation.

Lateral smoothing penalizes the difference between the anomaly at a knot and the average of the anomalies at its neighboring knots by minimizing the first and second spatial derivatives of velocity anomalies ((Lebedev and Van Der Hilst 2008; Lebedev et al. 2006; Wang and Dahlen 1995).

The inversion is stabilized by minimizing the first derivative of log(conductivity) with respect to log(depth).

The first stage optimizes a fault tolerance metric; the second improves scheduling by minimizing the latencies of the acknowledgment and retransmission messages.

Third is minimizing the effective population size.

Unlike the classical variational method to design the neighboring optimal control (NOC) by minimizing the second variation of cost functional, this paper, from a geometric point of view, presents a parametric approach to establish the NOC for the problem of fixed-time multi-burn orbital transfers.