Subgradient-Based Neural Networks for Nonsmooth Nonconvex Optimization Problems

This paper presents a subgradient-based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function, a class of affine equality constraints, and a class of nonsmooth convex inequality constraints. The proposed neural network is modeled with a diff...

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Vydáno v:IEEE transactions on neural networks Ročník 20; číslo 6; s. 1024 - 1038
Hlavní autoři: Bian, Wei, Xue, Xiaoping
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.06.2009
Institute of Electrical and Electronics Engineers
Témata:
Algorithm design and analysis
Algorithms
Application specific integrated circuits
Applied sciences
Artificial intelligence
Artificial neural networks
Computer networks
Computer science; control theory; systems
Computer Simulation
Computer systems and distributed systems. User interface
Connectionism. Neural networks
Constraint optimization
Convergence
Convergence in finite time
Design optimization
differential inclusion
Exact sciences and technology
Inclusions
Inequalities
Mathematical analysis
Mathematical models
Models, Theoretical
neural network
Neural network hardware
Neural networks
Neural Networks (Computer)
Nonlinear Dynamics
nonsmooth nonconvex optimization
Optimization
Parallel algorithms
Pattern Recognition, Automated - methods
Signal processing algorithms
slow solution
Software
Trajectories
Non convex programming
Critical point
Network management
Neural network
Set constraint
Convex programming
Global solution
slow solution
Equilibrium point
nonsmooth nonconvex optimization
Inequality constraint
Equality constraint
Convergence in finite time
Objective function
Differential inclusion
Non convex analysis
Inequality
Mathematical programming
ISSN:1045-9227, 1941-0093, 1941-0093
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Popis
Shrnutí:This paper presents a subgradient-based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function, a class of affine equality constraints, and a class of nonsmooth convex inequality constraints. The proposed neural network is modeled with a differential inclusion. Under a suitable assumption on the constraint set and a proper assumption on the objective function, it is proved that for a sufficiently large penalty parameter, there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter. It is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network, and coincides with the set which consists of the critical points of the objective function in the feasible region. A condition is given to ensure the convergence to the equilibrium point set in finite time. Moreover, under suitable assumptions, the coincidence between the solution to the differential inclusion and the ldquoslow solutionrdquo of it is also proved. Furthermore, three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network.
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ISSN:1045-9227
1941-0093
1941-0093
DOI:10.1109/TNN.2009.2016340