In this paper we study fuzzy multiobjective optimization problems defined for n variables. Based on a new p-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.

This paper aims to establish first-order necessary Optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems‎. ‎These problems involve inequality constraints whose index set depends on the decision vector‎, ‎and all emerging functions are assumed to be locally Lipschitz‎. ‎We introduce a new constraint qualification for these problems‎. ‎Building upon this qualification‎, ‎we derive an upper estimate for the Clarke sub-differential of the value function of the problem‎. ‎Furthermore‎, ‎we demonstrate the necessary Optimality conditions for properly efficient solutions to the problem‎.

In this paper, we consider fuzzy optimization problems more general than all those that exist in the literature by using the concept of metric-based differentiability of fuzzy-valued functions. We get necessary Optimality conditions based on fuzzy stationary point definition, and we prove these conditions are also sufficient under new fuzzy invexity notions. We illustrate these results with numerical examples.

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator function. Relation between weak subifferential and augmented normal cone and epigraph is also explored. We also obtain Optimality conditions via weak subdifferential and augmented normal cone. Finally, we define the Stampacchia and Minty solution via weak subdifferential and investigate the relation between Stampacchia and Minty solution and the minimal point.

The primary objective of this paper is to enhance several well-known geometric constraint qualifications and necessary Optimality conditions for nonsmooth semi-infinite optimization problems (SIPs). We focus on defining novel algebraic Mangasarian-Fromovitz type constraint qualifications, and on presenting two Karush-Kuhn-Tucker type necessary Optimality conditions for nonsmooth SIPs defined by locally Lipschitz functions. Then, by employing a new type of generalized invex functions, we present sufficient conditions for the Optimality of a feasible point of the considered problems. It is noteworthy that the new class of invex functions we considered encompasses several classes of invex functions introduced previously. Our results are based on the Michel-Penot subdifferential.

In this paper, necessary Optimality conditions for a class of optimal control problems containing time-varying delays in control and state variables are discussed. There is an important aspect of these problems in that time-varying delays are applied to both state and control variables. Also, the cost functional of problems is influenced by the time-varying delays in state and control. We prove necessary Optimality conditions in this study. A key aspect of the proof is calculating the variations of control and state variables when there are time-dependent delays. we make use of appropriate changing variables to derive these variations. In order to illustrate the use of these conditions, several examples are solved and numerical results are presented. At the end, some conclusions are drawn.

In the present paper, we show the some properties of the fuzzy solution of the control linear fuzzy differential equations and research the optimal time problems for it.

The aim of present paper is to study a constrained programming with generalized α − univex fuzzy mappings. In this paper we introduce the concepts of α − univex, α − preunivex, pseudo α − univex and α − unicave fuzzy mappings, and we discover that α − univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized α − univex fuzzy mappings and get some properties. In the last, we derive necessary and suffcient Karush-Kuhn-Tucker conditions and its dual problems with generalized differentiable α − univex fuzzy mappings for fuzzy constrained programming problem.