Time-varying nonlinear optimization problems with different noises often arise in the fields of scientific and engineering research. Noises are unavoidable in the practical workspace, but the most existing models for time-varying nonlinear optimization problems carry out with one assume that the computing process is free of noises. In this paper, from a control-theoretical framework, noise-suppressing zeroing neural dynamic (NSZND) model is developed, analyzed and investigated by feat of continuous-time zeroing neural network model, which behaves efficiently for hurdling online time-varying nonlinear optimization problems with the presence of different noises. Further, for speeding the rate of convergence, general noise-suppressing zeroing neural network (GNSZNN) model with different activation functions is discussed. Then, theoretical analyses show that the proposed noise-suppressing zeroing neural network model derived from NSZND model has the global convergence property in the presence of different kinds of noises. Besides, how GNSZNN model performs with different activation functions is also proved in detail. In addition, numerical results are provided to substantiate the feasibility and superiority of GNSZNN model for online time-varying nonlinear optimization problems with inherent tolerance to noises.

Noise-suppressing zeroing neural network for online solving time-varying nonlinear optimization problem: a control-based approach

The three-term conjugate gradient methods solving large-scale optimization problems are favored by many researchers because of their nice descent and convergent properties. In this paper, we extend some new conjugate gradient methods, and construct some three-term conjugate gradient methods. An remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition without any line search. Under the standard Wolfe line search, the global convergence properties of the proposed methods are proved merely by assuming that the objective function is Lipschitz continuous. Preliminary numerical results and comparisons show that the proposed methods are efficient and promising.

Some three-term conjugate gradient methods with the inexact line search condition

In this paper, we propose, analyze, and test an alternative method for solving the l 1 -norm regularization problem for recovering sparse signals and blurred images in compressive sensing. The method is motivated by the recent proposed nonlinear conjugate gradient method of Tang, Li and Cui [Journal of Inequalities and Applications, 2020(1), 27] designed based on the least-squares technique. The proposed method aims to minimize a non-smooth minimization problem consisting of a least-squares data fitting term and an l 1 -norm regularization term. The search directions generated by the proposed method are descent directions. In addition, under the monotonicity and Lipschitz continuity assumption, we establish the global convergence of the method. Preliminary numerical results are reported to show the efficiency of the proposed method in practical computation.

Least-Square-Based Three-Term Conjugate Gradient Projection Method for ℓ1-Norm Problems with Application to Compressed Sensing

Three-Term of New Conjugate Gradient Projection Approach under Wolfe Condition to Solve Unconstrained Optimization Problems

Some three-term conjugate gradient methods with the new direction structure

The conjugate gradient method is one of the most effective methods to solve the unconstrained optimization problems In this paper, we develop a new three-term conjugate gradient (TTCG) method by applying the Powell symmetrical technique to the Hestenes–Stiefel method The proposed method satisfies both the sufficient descent property and the conjugacy condition , which do not rely on any line search Under the standard Wolfe line search, the global convergence of the proposed method is also established The numerical results also show that the proposed method is very effective and interesting by comparing with other TTCG methods using a classical set of test problems

S. J. Li

Papers

New three-term conjugate gradient method with guaranteed global convergence