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The Shapley Folkman lemma has applications also in optimization and probability theory.
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Such sums of sets arise in economics, in mathematical optimization, and in probability theory; in each of these three mathematical sciences, non-convexity is an important feature of applications.
It has been previously demonstrated in [1, 2] that PST can be solved by several sparse recovery algorithms that fall into different categories, including augmented Lagrangian rank-minimization [1], ℓ 1 optimization approaches and probability-based methods [2].
The power-exponential functions have useful applications in mathematical analysis and in other theories like statistics, biology, optimization, ordinary differential equations, and probability [1].
The objective functions that are considered for such Pareto multi-objective optimization are namely, probability of failure of settling time (PTS) and probability of failure of overshoot (POS).
In this section, we discuss system performance evaluation in three aspects: downlink coverage probability, power consumption optimization, and energy efficiency.
Statistical convergence has several applications in different fields of mathematics: summability theory, number theory, trigonometric series, probability theory, measure theory, optimization, and approximation theory.
The weighting factor would be changed through optimization control probability.
To sum up, we can obtain the optimization control probability of the mobile crowd biological engineering such as equation (13).
Optimization of probability score.
Hence, the probability p0 is determined before starting the optimization and its value does no need to be updated at each iteration.
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