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Unfortunately, the exact maximization with respect to the unknown parameters is rather difficult and does not exist a close-form expression.
The maximization achievable rates using various transmission strategies can be performed also using the proposed algorithm based on alternative maximization with respect to symbol positions and the joint distribution of probability.
Likelihood maximization with respect to each of μ i, c i is a simple least-squares fitting, and can be done independently for each image location x i : μ ̂ i = y T ( x i ) 1 K (8).
Corley [1] proved that a maximization with respect to a cone, which subsumes ordinary and Pareto optimization, is equivalent to the problem of finding an endpoint of certain multivalued mapping.
Equation (4) establishes profit maximization with respect to the household choice of (x, F, H, L, y, N), with π( p, r, w, T - l) being the indirect profit function conditional on (T - l).
The Lagrangian function L p has to be minimized with respect to w and b and maximized with respect to α i ≥ 0. By using Karush-Kuhn-Tucker (KKT) conditions, the design variables w and b in Eq. 8 can be expressed in terms of α i, which then transforms the problem into a dual problem that requires only maximization with respect to the Lagrangian multipliers α i (9) (10).
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Thus the problem of determining a metabolic pathway yielding maximum rate of production of a metabolite B starting from a substrate A, boils down to a maximization problem, where z is maximized with respect to c, subject to satisfying the constraint given in Eq. (6).
According to the alternating maximization, a function can be cyclically maximized with respect to one (or a block of) variable, while keeping the other variables fixed.
Note also that the maximization is with respect to the power adaptation policies P1and P1and
The model is formulated as profit maximization problem with respect to the retailer and solved with the help of genetic algorithm (GA) and PSO.
The equality of the budget constraints allows to substitute out consumption and to restate the maximization problem with respect to the portfolio weights and initial consumption.
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