A Dai-Liao-type projection method for monotone nonlinear equations and signal processing
Copyright policy )A Dai-Liao-type projection method for monotone nonlinear equations and signal processing
Abstract In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ 1 {\ell }_{1} -norm regularized problems to decode sparse signals and images in compressive sensing.
- China Medical University China (People's Republic of)
- China Medical University Hospital Taiwan
- King Mongkut's University of Technology Thonburi Thailand
- Bayero University Kano Nigeria
- Usmanu Danfodiyo University Nigeria
Eigenvalues, singular values, and eigenvectors, Inverse Problems in Mathematical Physics and Imaging, Nonlinear conjugate gradient method, Economics, FOS: Political science, Norm (philosophy), compressive sensing, Computational Mechanics, 90c53, Engineering, Numerical mathematical programming methods, unconstrained optimization, Political science, Mathematical Physics, Numerical Analysis, Numerical Optimization Techniques, Physics, 65k05, Lipschitz continuity, Theory and Applications of Compressed Sensing, Regular polygon, Algorithm, conjugate gradient method, Physical Sciences, Convergence (economics), nonlinear equations, Compressed sensing, Monotonic function, Artificial neural network, 15a18, Convex Optimization, Dykstra's projection algorithm, 90c30, Geometry, FOS: Law, Conjugate gradient method, Mathematical analysis, Quantum mechanics, Nonlinear programming, Machine learning, QA1-939, FOS: Mathematics, Projection method, Orthogonal Matching Pursuit, Jacobian matrix and determinant, Economic growth, Gradient descent, Numerical methods based on nonlinear programming, projection method, 49m37, Projection (relational algebra), Methods of quasi-Newton type, Applied mathematics, Computer science, Nonlinear system, Monotone polygon, Law, Mathematics, Mixed-Integer Nonlinear Programs
Eigenvalues, singular values, and eigenvectors, Inverse Problems in Mathematical Physics and Imaging, Nonlinear conjugate gradient method, Economics, FOS: Political science, Norm (philosophy), compressive sensing, Computational Mechanics, 90c53, Engineering, Numerical mathematical programming methods, unconstrained optimization, Political science, Mathematical Physics, Numerical Analysis, Numerical Optimization Techniques, Physics, 65k05, Lipschitz continuity, Theory and Applications of Compressed Sensing, Regular polygon, Algorithm, conjugate gradient method, Physical Sciences, Convergence (economics), nonlinear equations, Compressed sensing, Monotonic function, Artificial neural network, 15a18, Convex Optimization, Dykstra's projection algorithm, 90c30, Geometry, FOS: Law, Conjugate gradient method, Mathematical analysis, Quantum mechanics, Nonlinear programming, Machine learning, QA1-939, FOS: Mathematics, Projection method, Orthogonal Matching Pursuit, Jacobian matrix and determinant, Economic growth, Gradient descent, Numerical methods based on nonlinear programming, projection method, 49m37, Projection (relational algebra), Methods of quasi-Newton type, Applied mathematics, Computer science, Nonlinear system, Monotone polygon, Law, Mathematics, Mixed-Integer Nonlinear Programs
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