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The upper bound and lower bound of the objective value are obtained by solving the pair of geometric programs.
A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the objective values.
Then, the minimization is executed over a convex lower bound of the objective function.
The LR can be seen as a broad range of techniques which supplies a lower bound of the objective function and good starting points for heuristic searches to obtain feasible primal solutions.
Using the fact that if X > 0 then tr (X-1) ≥ ∑ i 1/ X) i, i, the original optimization problem is simplified by minimizing the lower bound of the objective function.
Since the proposed objective function is not convex, we further derive a lower bound of the objective function to make it convex which is different from the upper bound in [14].
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The entropy is the difference between the upper bound and the lower bound of the profit objective.
By weak duality, the optimal value serves as a lower bound of the dual objective value.
An exact complexity analysis, and the choice of the tolerance to compute a solution within a certain bound of the optimal objective function are possible [20].
It is a global lower bound of the nonconcave objective function F, i.e., begin{array}{*{20}l} F^{ kappa)}(mathbf{x},mathbf{y}) &leq F(mathbf{x},mathbf{y}), forall (mathbf{x},mathbf{y}).
end{array} (27) It is a global lower bound of the nonconcave objective function F, i.e., begin{array}{*{20}l} F^{ kappa)}(mathbf{x},mathbf{y}) &leq F(mathbf{x},mathbf{y}), forall (mathbf{x},mathbf{y}).
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bound of the Laplacian
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