Some Convergence Properties of the Steepest Descent Algorithm Revealed by Renormalisation

2001 ◽  
pp. 459-471
Author(s):  
Luc Pronzato ◽  
Henry P. Wynn ◽  
Anatoly A. Zhigljavsky
Keyword(s):  
Steepest Descent ◽  
Convergence Properties ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

Variable leaky steepest descent algorithm for autoregressive fading estimation in OFDM systems

2021 ◽  
pp. 103169
Author(s):  
Mohammad Ghanavati Mohammadi ◽  
Alimorad Mahmoudi ◽  
Abdolnabi Kosarian
Keyword(s):  
Steepest Descent ◽  
Ofdm Systems ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm ◽  
Fading Estimation

scholarly journals Local Search Algorithms for the Beam Angles’ Selection Problem in Radiotherapy

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Guillermo Cabrera-Guerrero ◽  
Nibaldo Rodriguez ◽  
Carolina Lagos ◽  
Enrique Cabrera ◽  
Franklin Johnson
Keyword(s):  
Radiation Therapy ◽  
Local Search ◽  
Organs At Risk ◽  
Treatment Plan ◽  
Search Algorithms ◽  
Steepest Descent ◽  
Beam Angle ◽  
Local Search Algorithms ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.

scholarly journals A time difference of arrival/angle of arrival fusion algorithm with steepest descent algorithm for indoor non-line-of-sight locationing

2019 ◽  
Vol 15 (9) ◽  
pp. 155014771986035 ◽  
Author(s):  
Chong Shen ◽  
Chengxiao Wang ◽  
Kun Zhang ◽  
Xianpeng Wang ◽  
Jing Liu
Keyword(s):  
Steepest Descent ◽  
Time Difference ◽  
Line Of Sight ◽  
Angle Of Arrival ◽  
Fusion Algorithm ◽  
Time Difference Of Arrival ◽  
Positioning Accuracy ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm ◽  
Non Line Of Sight

In complex indoor propagation environment, the non-line-of-sight error caused by various obstacles brings great error to node positioning. Choosing the appropriate signal transmission methods is important to improve node indoor positioning accuracy. In this research, ultra-wideband technology, as baseband with high theoretical positioning accuracy and real-time performance, is implemented to transmit indoor signals. The proposed fusion algorithm with ultra-wideband baseband takes advantages from both time difference of arrival and angle of arrival algorithms, combined through the steepest descent algorithm. The non-line-of-sight signal estimation error is iteratively eliminated to achieve effective positioning accuracy. The experimental results indicate that the novel time difference of arrival/angle of arrival fusion algorithm with steepest descent algorithm can largely improve node positioning accuracy and stability.

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