Inverse incomplete gamma function and its application

Dohler, Mischa; Arndt, Marylin

doi:10.1049/el:20063446

Cited by 32 publications

(14 citation statements)

References 2 publications

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“…To show a contradiction, assume that the cost converges to a finite value instead of −∞. From the Armijo condition, (5), and because the sequence is nonincreasing, J(x j [i + 1]) − J(x j [i]) must equal zero, implying that ∇J(x j [i]) J (x j [i]) = 0. If ∇J(x j [i]) = 0, then the step size would go to zero contradicting that a limit cycle was reached.…”

Section: Discussionmentioning

confidence: 99%

Optimal Inverse Functions Created via Population-Based Optimization

Jennings

Ordóñez

2014

IEEE Trans. Cybern.

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Finding optimal inputs for a multiple-input, single-output system is taxing for a system operator. Population-based optimization is used to create sets of functions that produce a locally optimal input based on a desired output. An operator or higher level planner could use one of the functions in real time. For the optimization, each agent in the population uses the cost and output gradients to take steps lowering the cost while maintaining their current output. When an agent reaches an optimal input for its current output, additional agents are generated in the output gradient directions. The new agents then settle to the local optima for the new output values. The set of associated optimal points forms an inverse function, via spline interpolation, from a desired output to an optimal input. In this manner, multiple locally optimal functions can be created. These functions are naturally clustered in input and output spaces allowing for a continuous inverse function. The operator selects the best cluster over the anticipated range of desired outputs and adjusts the set point (desired output) while maintaining optimality. This reduces the demand from controlling multiple inputs, to controlling a single set point with no loss in performance. Results are demonstrated on a sample set of functions and on a robot control problem.

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Section: Discussionmentioning

confidence: 99%

Optimal Inverse Functions Created via Population-Based Optimization

Jennings

Ordóñez

2014

IEEE Trans. Cybern.

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“…To simplify further analysis, some approximations to the outage probability are invoked that permit the derivation of a near-optimal closedform power allocation solution. Following the approximation method given in [7], [14], the outage probability p out,k,j (t …”

Section: Problem Simplificationmentioning

confidence: 99%

Power Allocations for Adaptive Distributed MIMO Multi-Hop Networks

Lang¹,

Wübben²,

Kammeyer³

2009

2009 IEEE International Conference on Communications

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Abstract-Distributed MIMO multi-hop relaying is one of the most promising technologies that permits cost-effective improvement of coverage, data rate and end-to-end (e2e) user experience by utilizing distributed low-complexity space-time codes to overcome path losses and deep fades of wireless channels. However, an efficient transmission scheme and resource management are required to exploit these advantages. Specifically, low-complexity adaptive schemes and power control strategies should be designed, thereby achieving robust and cost-efficient e2e communications. In this paper an adaptive transmission scheme is presented, where one relay stops forwarding the message if it is in outage and other nodes adapt to a new spacetime code. For this adaptive scheme, optimal as well as suboptimal closed-form power allocation solutions are derived which minimize the total transmission power while satisfying a given e2e outage probability. The significant power savings due to the proposed approaches in comparison to a non-adaptive scheme is demonstrated by numerical results.

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“…Following the approximation method given in [2], [9], the outage probability p out,k,j (t k ) in (3) is upper bounded for high SNR as…”

Section: Problem Simplificationmentioning

confidence: 99%

Joint Power and Time Allocation for Adaptive Distributed MIMO Multi-Hop Networks

Lang¹,

Wübben²,

Kammeyer³

2009

VTC Spring 2009 - IEEE 69th Vehicular Technology Conference

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Distributed MIMO multi-hop relaying can provide cooperative diversity and overcome path losses, hence, boost the end-to-end (e2e) performance. By using a low-complexity adaptive scheme, where one relay stops sending the message if it is in outage and other nodes adapt to a new space-time code, robust communication links can be further achieved. The contribution of this paper is the derivation of near-optimal closed-form solution for joint power and time allocation for such adaptive scheme that minimizes he transmission power while satisfying a given e2e non-ergodic outage probability.

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Inverse incomplete gamma function and its application

Cited by 32 publications

References 2 publications

Optimal Inverse Functions Created via Population-Based Optimization

Optimal Inverse Functions Created via Population-Based Optimization

Power Allocations for Adaptive Distributed MIMO Multi-Hop Networks

Joint Power and Time Allocation for Adaptive Distributed MIMO Multi-Hop Networks

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