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Optimal portfolios are here based on maximizing the lower price of the portfolio.
In fact, some family of Q distributions can be chosen and the best approximation within this family is found by maximizing the lower bound with respect to Q.
For maximizing the lower bound and re-estimating the parameters, we have a constrained optimization problem because all parameters indicate probability distributions.
In our first algorithm, following existing single-threshold rank detection scheme, we rigorously derive an analytical lower bound on the correct rank detection probability and propose a systematic threshold selection method by maximizing the lower bound.
For the two new multiple-threshold schemes, different thresholds are used for different possible rank values, and each threshold is derived by maximizing the lower bound on the probability of correct rank detection when a specific rank value is assumed.
This shows that maximizing the lower bound (mathcal {L} eta,phi,zeta ;alpha,beta,mu _{1 C},sigma _{1 C})) with respect to is equivalent to minimizing the above KL divergence.
Similar(49)
Specifically, the objective of locating the facilities is to maximize the lower limit of future earnings based on a stated confidence level.
Thus, for some fixed value of, we can directly apply (35) to maximize the lower bound (28).
Thus, we can also maximize the lower bound (mathcal {L} eta,phi,zeta ;alpha,beta,mu _{1 C},sigma _{1 C})) with respect to the parameters {α,β,μ 1 C,σ 1:C }.
As will be shown in the simulation results, even with the sub-optimal approach which maximizes the lower bound, the proposed method can achieve performance similar to the optimal solution obtained by exhaustive search.
Numerical power allocation (Numerical-PA), with the values of αtand βtobtained by a numerically exhaustive search to maximize the lower bound on the training-based achievable rate in (23).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com