A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Problems With Equality and Inequality Constraints

Abstract

Pseudoconvex optimization problem, as an important nonconvex optimization problem, plays an important role in scientific and engineering applications. In this paper, a recurrent one-layer neural network is proposed for solving the pseudoconvex optimization problem with equality and inequality constraints. It is proved that from any initial state, the state of the proposed neural network reaches the feasible region in finite time and stays there thereafter. It is also proved that the state of the proposed neural network is convergent to an optimal solution of the related problem. Compared with the related existing recurrent neural networks for the pseudoconvex optimization problems, the proposed neural network in this paper does not need the penalty parameters and has a better convergence. Meanwhile, the proposed neural network is used to solve three nonsmooth optimization problems, and we make some detailed comparisons with the known related conclusions. In the end, some numerical examples are provided to illustrate the effectiveness of the performance of the proposed neural network.

A projection-based continuous-time algorithm for distributed optimization over multi-agent systems

“…It is worth noting that the property of entering one of the constraints or feasible region is possessed by many continuous-time algorithms for solving optimization problems, such as [8,11,19,34]. This proposition guarantees the continuous-time algorithm (17) which has the advantages of simplifying the distributed optimization problems by ignoring one of the constraints once the states enter this set.…”

“…Remark 2 Penalty method is a widely adopted approach in solving optimization problems with sorts of constraints, such as [19,28] and so on. By introducing penalty parameters, one can reduce the dimension of related algorithms.…”

GMDS-ZNN Model 3 and its Ten-Instant Discrete Algorithm for Time-Variant Matrix Inversion Compared With Other Multiple-Instant Ones

“…Content may change prior to final publication. With (5) and (10), the six-instant DTVMI algorithm is named as DTVMI-III algorithm, which is given as follows:…”

“…Methods based on RNN have manifested their high-speed parallelprocessing nature and convenience of hardware implementation [5], [6]. They have been motivated as analog machines to solve optimization problems [7]- [10]. In 2001, aiming at the online solution of various time-variant problems, a new class of RNN, termed Zhang neural network (ZNN), has been proposed in [11].The ZNN model is essentially based on an indefinite function termed Zhang function (ZF) which is served as error-monitoring.…”

Design and Analysis of Two FTRNN Models With Application to Time-Varying Sylvester Equation

“…As we know the convergence performance of a RNN can be improved significantly by selecting proper activation function, and several novel activation functions are presented in recent year [19], [20]. Unlike the thought of developing activation functions, this paper focuses on improving the ZNN model to accelerate its convergence performance.…”