This paper addresses a non-smooth multi-objective semi-infinite programming problem that involves a feasible set defined by inequality CONSTRAINTs‎. ‎Our focus is on introducing a new weak Slater CONSTRAINT QUALIFICATION and deriving the necessary and sufficient conditions for (weakly‎, ‎properly) efficient solutions to the problem using (weak and strong) Karush-Kuhn-Tucker types‎. ‎Additionally‎, ‎we present two duals of the Mond-Weir type for the problem and provide (weak and strong) duality results for them‎. ‎All of the results are given in terms of Clarke subdifferential‎.

In this paper, we consider the semi-infinite programming problems with non-differentiable emerging functions. Firstly, we give a counterexample showing that Theorem 3.1 of Ref. [10] is not true. Then, by modifying the assumptions of this theorem, we establish a new necessary Theorem for optimal solution of the problem.

In this paper, we consider a nonsmooth multiobjective problem with equilibrium CONSTRAINTs (MPEC). We present three CONSTRAINT QUALIFICATIONs (CQs) and investigate their relations. Furthermore, we derive two types of necessary optimality conditions under these CQs.

In this paper an uncertain multi objective closed-loop supply chain is developed. The first objective function is maximizing the total profit. The second objective function is minimizing the use of row materials. In the other word, the second objective function is maximizing the amount of remanufacturing and recycling. Genetic algorithm is used for optimization; and for finding the pareto optimal line, Epsilon-CONSTRAINT method is used. Finally a numerical example is solved with proposed approach and performance of the model is evaluated in different sizes. The results show that this approach is effective and useful for managerial decisions.

This paper studies the convex multiobjective optimization problem with vanishing CONSTRAINTs. We introduce a new CONSTRAINT QUALIFICATION for these problems, and then a necessary optimality condition for properly efficient solutions is presented. Finally by imposing some assumptions, we show that our necessary condition is also sufficient for proper efficiency. Our results are formulated in terms of convex subdifferential.

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 as 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.

It is necessary to pay attention to the tax system, both in terms of laws and in terms of organization, with the aim of influencing the long-term economic orientation, financing the government, and ultimately helping to realize the economic development strategy. Meanwhile, effective use of human resources is an indicator without which economic development is not possible and according to the organizational factors, the country can be properly managed by relying on tax revenues. In fact, the productivity of human resources in organizations is one of the characteristics of today’s advanced societies. In the meantime, competence and job satisfaction can be one of the most important and influential factors in organizational performance. Considering the importance of human resources in the success of today’s organizations, this study aims at investigating the effect of individual competence and job satisfaction of tax auditors on the taxable power of the tax administration and also to examine this effect in the presence of time pressure. The statistical population of this study includes all tax auditors in 2020 who were randomly selected and finally 348 samples were selected to test the hypotheses and they were analyzed using structural equation modeling in PLS software. The results of testing the hypotheses have shown that the individual competence of the tax auditor has a significant and positive effect on the taxable power. Similarly, the power of taxation increases with the job satisfaction of tax auditors. While individual competence and job satisfaction of tax auditors in the presence of time CONSTRAINTs (pressure) has no significant effect on the power of taxation.

In this paper, the class of nonconvex vector-valued optimization problems with inequality CONSTRAINTs is considered. We introduce two CONSTRAINT QUALIFICATIONs and derive the weak and strong Karush-Kuhn-Tucker type of necessary conditions for a (weakly) efficient solution to the considered problem. All results are given in terms of Dini directional derivative and Clarke subdifferential.

This paper is devoted to the study of locally Lipschitz semi-infinite programming problems in which the index set of the inequality CONSTRAINTs is assumed to be arbitrary. We introduce an analogous of the Arrow-Hurwitcz-Uzawa CONSTRAINT QUALIFICATION which is based on the Clarke subdifierential. Then, we derive a Karush-Kuhn-Tucker type necessary condition. Finally, interrelations between the new and the Slater CONSTRAINT QUALIFICATIONs are investigated.