SINR maximization in MIMO radars using Riemannian quasi-Newtown optimization
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This paper focus on the waveform design of multiple-input multiple-output (MIMO) under the practical constraint of constant modulus (CM), aims to maximize the Signal-to-Interference-plus-Noise Ratio (SINR) of radar receiver output in the worst case by radiation nulls generation. Because of the CM constraint, the issue is nonconvex and NP-hard. We find that Limited-memory BFGS algorithm is suitable for solving the quadratic optimization problem and the CM constraint is equal to the feasible set on the complex circle manifold. Numerical results demonstrate that our method is superior to recent comparison methods.Keywords:
Broyden–Fletcher–Goldfarb–Shanno algorithm
Maximization
Signal-to-interference-plus-noise ratio
Broyden–Fletcher–Goldfarb–Shanno algorithm
Line search
Quasi-Newton method
Line (geometry)
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In this paper, we propose an iterative subchannel selection scheme for distributed signal to inteference and noise ratio (SINR) maximization in multiple-input multiple-output (MIMO) interference channels. At each iteration of the proposed scheme, each user chooses the predetermined number of subchannels to maximize its own information rate in a distributed way. Numerical results are presented to verify the performance enhancement of the proposed subchannel selection.
Maximization
Signal-to-interference-plus-noise ratio
Interference Alignment
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The BFGS quasi-Newton methodology, popular for smooth minimization, has also proved surprisingly effective in nonsmooth optimization. Through a variety of simple examples and computational experiments, we explore how the BFGS matrix update improves the local metric associated with a convex function even in the absence of smoothness and without using a line search. We compare the behavior of the BFGS and Shor r-algorithm updates.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Quasi-Newton method
Smoothness
Line search
Matrix (chemical analysis)
Minification
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In this article, we propose a classical optimization algorithm named L-BFGS to simulate the thermal behavior of electron gun for terahertz traveling-wave tubes. The L-BFGS algorithm, as a variation of Quasi-Newton optimization method, expert in dealing with the unconstrained optimization problems while keeping the stability of the calculation. Efficiency and accuracy of L-BFGS algorithm are verified by modeling the thermal behavior of an actual electron gun on MATLAB platform successfully with no breakdown. According to the simulation results, this method performs better than some reference methods in terms of computational memory usage and time cost. Our numerical conclusions indicate that it is promising for thermal analysis of electron gun, which would be useful for researchers during the design phase.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Electron gun
Coaxial
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Broyden–Fletcher–Goldfarb–Shanno algorithm
Line search
Complex system
Line (geometry)
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A class of modified BFGS method based on the new quasi-Newton equation is presented in this paper to solve the unconstrained optimization problem.We also propose a modified BFGS method based on XIAO's modified BFGS method and LIAO's modified method.By choosing the proper parameters,we can prove that the new method has global and superlinear convergence properties under suitable conditions.Besides,numerical testing results are given to prove its superiority.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Quasi-Newton method
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This paper studies some possible combinations of the best features of the quasi-Newton symmetric rank-one (SR1), BFGS and extra updating BFGS algorithms for solving nonlinear unconstrained optimization problems. These combinations depend on switching between the BFGS and SR1 updates so that certain desirable properties are imposed. The presented numerical results show that the proposed switching algorithm outperforms the robust BFGS method.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Rank (graph theory)
Quasi-Newton method
Optimization algorithm
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In this paper an hybrid CG direction and a modified direction of the Storey's projected version of the BFGS Quasi-Newton (QN) update of optimization is investigated theoretically and experimentally. The new proposed algorithm is compared with. Storey's projected BFGS method on a large number of standard test functions with dimensionality varies between 4≤ n≤ 1000. The new algorithm is found to be superior to the Storey's projected BFGS method overall but it showed a considerable superiority on some of test functions. ــــــــــــــــ
Broyden–Fletcher–Goldfarb–Shanno algorithm
Minification
Quasi-Newton method
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Recently, several modification techniques have been introduced to the line search BFGS method for solving unconstrained optimization problems. We present a modified BFGS method for solving symmetric nonlinear equations. The numerical results show that the approach to be reliable and efficient.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Quasi-Newton method
Line search
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The BFGS method is one of the most effective quasi-Newton algorithms for minimization-optimization problems. In this paper, an improved BFGS method with a modified weak Wolfe–Powell line search technique is used to solve convex minimization problems and its convergence analysis is established. Seventy-four academic test problems and the Muskingum model are implemented in the numerical experiment. The numerical results show that our algorithm is comparable to the usual BFGS algorithm in terms of the number of iterations and the time consumed, which indicates our algorithm is effective and reliable.
Broyden–Fletcher–Goldfarb–Shanno algorithm
Quasi-Newton method
Line search
Minification
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