Joint transmit and receive beamforming for MIMO interference channels using the difference of convex programming

2021 ◽  
Author(s):  
Negin Danesh ◽  
Mansour Sheikhan ◽  
Behrad Mahboobi
Keyword(s):  
Convex Programming ◽  
Interference Channels ◽  
Difference Of Convex Programming ◽  
Difference Of Convex ◽  
The Difference ◽  
Mimo Interference Channels

scholarly journals An Accelerated Proximal Algorithm for the Difference of Convex Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Feichao Shen ◽  
Ying Zhang ◽  
Xueyong Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Optimization Problem ◽  
Proximal Algorithm ◽  
Proximal Point ◽  
Difference Of Convex Programming ◽  
Difference Of Convex ◽  
The Difference ◽  
The Given ◽  
Dc Decomposition

In this paper, we propose an accelerated proximal point algorithm for the difference of convex (DC) optimization problem by combining the extrapolation technique with the proximal difference of convex algorithm. By making full use of the special structure of DC decomposition and the information of stepsize, we prove that the proposed algorithm converges at rate of O 1 / k 2 under milder conditions. The given numerical experiments show the superiority of the proposed algorithm to some existing algorithms.

scholarly journals Synthesizing Invariant Barrier Certificates via Difference-of-Convex Programming

2021 ◽  
pp. 443-466
Author(s):  
Qiuye Wang ◽  
Mingshuai Chen ◽  
Bai Xue ◽  
Naijun Zhan ◽  
Joost-Pieter Katoen
Keyword(s):  
Convex Programming ◽  
Time Horizon ◽  
Optimization Problems ◽  
Global Optimum ◽  
Divide And Conquer ◽  
Local Optimum ◽  
Difference Of Convex Programming ◽  
Weak Completeness ◽  
Completeness Result ◽  
Difference Of Convex

AbstractA barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over the infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses unbounded-time safety of differential dynamical systems. The proposed condition is by far the least conservative one on barrier certificates, and can be shown as the weakest possible one to attain inductive invariance. We show that discharging the invariant barrier-certificate condition—thereby synthesizing invariant barrier certificates—can be encoded as solving an optimization problem subject to bilinear matrix inequalities (BMIs). We further propose a synthesis algorithm based on difference-of-convex programming, which approaches a local optimum of the BMI problem via solving a series of convex optimization problems. This algorithm is incorporated in a branch-and-bound framework that searches for the global optimum in a divide-and-conquer fashion. We present a weak completeness result of our method, in the sense that a barrier certificate is guaranteed to be found (under some mild assumptions) whenever there exists an inductive invariant (in the form of a given template) that suffices to certify safety of the system. Experimental results on benchmark examples demonstrate the effectiveness and efficiency of our approach.

scholarly journals Gray Box Identification Using Difference of Convex Programming

2017 ◽  
Vol 50 (1) ◽  
pp. 9462-9467 ◽  
Author(s):  
Chengpu Yu ◽  
Lennart Ljung ◽  
Michel Verhaegen
Keyword(s):  
Convex Programming ◽  
Difference Of Convex Programming ◽  
Difference Of Convex
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