Research On Neurodynamic Approaches For Several Nonsmooth Optimization Problems

Nonsmooth optimization problems are widely used in many fields such as production planning and engineering practice.Since the analyticity of objective and constraint functions can not be well guaranteed,the research on nonsmooth optimization problems is relatively under-developed.The continuous improvement and development of differential inclusion theory and Clarke’s generalized gradient provide powerful theoretical guidance for the method design of this kind of problems.Meanwhile,since recurrent neural networks are capable of both parallel computation and distributed processing of data information,and the computational speed of the solution process does not decrease with the increase of the problem scale,neurodynamic approaches based on them have attracted much attention in the field of real-time solving complex optimization problems in recent years.In this paper,the corresponding neurodynamic approaches are proposed for nonsmooth pseudoconvex optimization,distributed fuzzy convex optimization,nonconvex optimization in quaternion domain,intelligent and connected vehicles power consumption optimization,and moreover,the feasibility and effectiveness of these approaches are guaranteed through strict theoretical analysis.The main contents of this dissertation are as follows:1.A single-layer projection neurodynamic model is proposed for solving a class of nonsmooth pseudoconvex optimization problems with linear equality and convex inequality constraints.Under the action of the projection operator,the state solution of the neurodynamic algorithm gradually approaches the simple constraint set in the inequality constraint set.With the help of Tikhonov regularization method,the algorithm does not need to calculate the exact penalty parameters.Based on differential inclusion theory and set-valued analysis,it is known that the state solution of the algorithm exists globally and is bounded.The finite-time convergence of the state solution to the feasible region and the global convergence to the optimal solution are proved by nonsmooth analysis.By comparing with several existing recurrent neural network approaches,the effectiveness of the proposed neurodynamic algorithm is verified by numerical examples.In addition,the algorithm has been applied to two practical problems related to pseudoconvex optimization.2.Based on the differential inclusion framework,Clarke’s generalized gradient is introduced to develop a neurodynamic approach for a class of constrained nonsmooth distributed fuzzy convex optimization problems.In this algorithm,partial order relation and closed convex set constraint are dealt with penalty method,the preestimation of penalty parameters is not introduced,and meanwhile the state solution can enter the constrained feasible region in a finite time and never leave.Furthermore,an equivalence relation between the equilibrium point of the neurodynamic system and the optimal solution of the distributed fuzzy convex optimization problem is given,and the convergence of the state solution to the optimal solution is proved.The theoretical results of the algorithm are verified by a numerical example and an optimization application of intelligent ship integrated energy system.3.A class of nonsmooth and nonconvex quaternion-variable optimization problems is investigated.By developing differential inclusion theory on quaternion domain,a quaternion-valued neurodynamic algorithm based on generalized quaternion gradient is constructed.The design of the algorithm does not need to split the quaternion variables in the optimization problem,but directly executes the update strategy on the quaternion state variable in the optimization process,which guarantees the integrity of the original problem structure.The global convergence of the algorithm to the set of critical points for nonconvex optimization problems with quaternion variables is proved mathematically,and the relevant theoretical results are established on quaternion domain.The effectiveness of the algorithm is verified by numerical examples and the attitude estimation of micro quadrotor.4.The power consumption optimization problem of intelligent and connected vehicles in the process of video information source data acquisition,compression coding,transmission and reception is studied.All vehicles and their interactions are regarded as a cooperative control system,each intelligent and connected vehicle corresponds to a node in the communication network,and the sum of all vehicles’ power consumption cost functions constitutes the global objective of this optimization problem.Based on the characteristics of distributed parallel computing of recurrent neural networks,a neurodynamic approach is designed and its global convergence is analyzed strictly.The theoretical results and simulation experiment show that all intelligent and connected vehicles finally reach consensus at the optimal power consumption under the action of this neurodynamic algorithm.