Control and Optimization in Applied Mathematics
Volume:6 Issue: 2, Summer-Autumn 2021

The present study introduces a kind of fractional-order Hopfield neural network (FOHNN)‎, ‎and its complex dynamic behavior is investigated through chaos analyses‎. ‎With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that for the values of 0.87 < α < 1‎, as the fractional-order (FO)‎, ‎the dynamical behavior of the mentioned FOHNN is chaotic‎. ‎Then‎, ‎the bounded trait of chaotic systems is utilized to derive an adaptive model-free control technique to suppress of complex dynamics of the FOHNN‎. ‎Furthermore‎, ‎according to the matrix analysis theorem of non-integer-order systems and the adaptive model-free control methodology‎, ‎analytical consequences of the designed controller are evidenced‎. ‎Eventually‎, ‎two examples are reported to illustrate the applicability of the mentioned model-free control method.

In this paper‎, ‎some constraint qualifications ‎of‎ the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints‎. ‎Then‎, ‎a new type of stationary condition‎, ‎named parametric stationary condition‎, ‎is presented for the problem‎, ‎and it is shown that all the stationarity conditions in various papers can be deduced from it‎. ‎This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case‎. ‎Finally‎, ‎the article ends with two important examples‎. ‎The results of the article are formulated according to Clark subdifferential and using nonsmooth analysis methods.

Classification is a crucial process in data mining‎, ‎data science‎, ‎machine learning‎, ‎and the applications of natural language processing‎. ‎Classification methods distinguish the correlation between the data and the output classes‎. ‎In single-label classification (SLC)‎, ‎each input sample is associated with only one class label‎. ‎In certain real-world applications‎, ‎data instances may be assigned to more than one class‎. ‎The type of classification which is required in such applications is known as multi-label classification (MLC)‎. ‎In MLC‎, ‎each sample of data is associated with a set of labels‎. ‎Due to the presence of multiple class labels‎, ‎the SLC learning process is not applicable to MLC tasks‎. ‎Many solutions to the multi-label classification problem have been proposed‎, ‎including BR‎, ‎FS-DR‎, ‎and LLSF‎. ‎But‎, ‎these methods are not as accurate as they could be‎. ‎In this paper‎, ‎a new multi-label classification method is proposed based on graph representation‎. ‎A feature selection technique and the Q-learning method are employed to increase the accuracy of the proposed algorithm‎. ‎The proposed multi-label classification algorithm is applied to various standard multi-label datasets‎. ‎The results are compared with state-of-the-art algorithms based on the well-known performance evaluation metrics‎. ‎Experimental results demonstrated the effectiveness of the proposed model and its superiority over the other methods.

In this article‎, ‎we offer an efficient method to find an approximate solution for quadratic optimal control problems‎. ‎The approximate solution is offered in a finite series form in reproducing kernel space‎. ‎The convergence of proposed method is analyzed under some hypotheses which provide the theoretical basis of the proposed method for solving quadratic optimal control problems‎. ‎Furthermore‎, ‎in this study‎, ‎we investigate the application of the proposed method to obtain the solution of equations that have formally been solved using Pontryagin's maximum principle‎. ‎Moreover‎, ‎many different types of quadratic optimal control problems are considered prototype examples‎. ‎The‎ ‎obtained results demonstrate that the proposed method is truly effective and‎ ‎convenient to obtain the analytic and approximate solutions of quadratic optimal control problems.

In this research‎, ‎we use averages and relative measures of interval grey numbers to introduce grey vertices, ‎grey edges‎, ‎and grey graphs (graphs are based on interval grey numbers)‎. ‎To do so‎, ‎we design a grey graph based on a graph (as the underlying graph)‎. ‎Also‎, ‎we find a relation between grey vertices and grey edges of a grey graph‎. ‎The primary method used in this research is based on linear inequalities related to grey vertices and grey edges‎. ‎We find some necessary and sufficient conditions on the grey vertex (as (non-)discrete grey vertices) connectivity of grey graphs based on interval grey numbers and linear inequality systems}.‎The paper includes implications for the development of(non-)weighted graphs‎, ‎and the modeling of uncertainty problems by grey vertices‎, ‎grey edges‎, ‎and their relations in a grey model as a grey graph‎. ‎As a weighted graph‎, ‎a fuzzy graph is a vital graph that has some applications in the real world‎, ‎but with changes in conditions‎, ‎it loses its efficiency‎. ‎On the other hand‎, ‎the efficiency of a grey graph is stable under changes in the conditions‎. ‎So‎, ‎grey graphs cover the weaknesses of fuzzy graphs‎. ‎The new conception of grey graphs based on grey numbers is introduced in this study‎. ‎We propose an optimization method that can be applied for grey numbers in an extension of graphs‎, ‎and apply it for gray numbers in the real world, especially for optimization problems and via gray graphs.

The aim of this paper is to assess and optimize the interaction of stakeholders in the lean management process via a dynamic game theory approach within the National Southern Oilfields Company. The present research is applied in terms of the purpose, and qualitative in terms of the data. Also, in terms of its nature and the implementation method, it is based on foundational data. To form the framework of the optimal stakeholder interaction management strategy and measure its effects on lean management (including the dimensions of components and indicators, etc.), scientific and legal documents were studied, experts who utilized the Delphi technique were interviewed, relevant data were summarized and, focus groups and brainstorming were held based on the data foundation method. The findings revealed that the organization in charge of the game selected Stackelberg’s game instead of Nash's game, since compared to the latter, the former could produce more than twice when it came to total profit, production of suppliers and manufacturers, etc., thus showing a 100% improvement compared to the cooperative games. In fact, in this study, the manufacturer under consideration preferred Stackelberg's game with the manufacturer acting as the leader and making decisions independent of the suppliers, gaining more profit and consequently more acceptance among people because of optimal production. In this model, three types of parameters played a key role in obtaining the outputs, the first of which was the cost of production. The rise in this parameter indicated the level of competition in profit and production. The second effective parameter was the coefficient of sensitivity to the level of demand for goods. An increase in this parameter caused a decrease in the profit and production of all members of the supply chain. Finally, the last effective parameter was the share of the base goods.