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The multi-objective minimization problem is formulated to minimize the function J (18) subject to the constraints mentioned in (3)–(7), (11)–(13) and an extra constraint as follow: sumlimits_{i = 1}^{4} {h_{i} } = 1quad h_{i} in left[ {begin{array}{*{20}c} 0 & 1 end{array} } right] (19).
To minimize the function of loss circulation, two optimizing algorithms are examined.
Our first approach to optimizing stability is to directly minimize the function α(A x)).
The objective of districting is to maximize or minimize the function of the weights between different districts.
New optimization point and direction which is conducive to minimize the function value are determined by the former search method after searching n th axis directions.
Increasing these gains tends to minimize the function (omega (t)) as a whole, which is indirectly linked to the inverse of the parametric "speed" of the curve.
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Thus, we search for the value of (varvec{lambda }) that minimizes the function (F varvec{lambda })).
By minimizing the function, we get the next expression for the orientation (18).
N1,..., N P is equivalent to minimizing the function, where N= [N1... N P ]T.
Consequently, if is a multiple of P then, the solution of minimizing the function in ℝ P coincides the solution of minimizing the function f(N) in ℕ P. Thus, the optimal placement minimizing the MSRL is.
The above formula for the Riemannian gradient now allows to implement the geometric CG algorithm for minimizing the function g2as define in (14) in a straightforward way.
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