In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty Vector variational-like inequality,  the Stampacchia Vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the Vector variational-like inequalities and Vector optimization problems are established.

In this article, we examine a nonsmooth Vector optimization problem with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type Vector variational inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth Vector optimization problems using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings.

In this paper, we establish weak and strong duality theorems for a pair of multi-objective symmetric dual problems. This removes several omissions in the paper "Symmetric and self-duality in Vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

This paper aims to study Vector optimization through improvement sets in locally convex spaces. This investigation could be viewed as an extension of the work of Lalitha and Chatterjee (J Optim Theory Appl 166: 825– 843, 2015) who studied an open problem on stability posed by Chicco et al., in normed linear spaces. This paper also establishes some existence results for this kind of Vector optimization using the celebrated KKM theorem (or Fan’ s Lemma, which is more common in the literature). Some examples illustrating the advantage of this work than that of Lalitha and Chatterjee (2015) are included too.

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.

The present study attempted to utilize a computational investigation to optimize the external freestream flow influence on thrust-Vector control. The external flow with different Mach numbers from 0. 05 to 1. 1 and with optimum injection angles from 60° to 120° were studied at variable flow conditions. Simulation of a converging-diverging nozzle with shock-Vector control method was performed, using the unsteady Reynoldsaveraged Navier-Stokes approach with Spalart-Allmaras turbulence model. This research established that freestream flow and fluidic-injection angle are the significant parameters on shock-Vector control performance. Computational results indicate that, increasing freestream Mach number would decline the thrust Vectoring effectiveness. Also, optimizing injection angle would reduce the negative effect of external freestream flow on thrust-Vector control. Moreover, increasing secondary to primary total pressure ratios and decreasing nozzle pressure ratios at different freestream Mach number would decrease dynamic response of starting thrust-Vector control. Additionally, to lead the improvement of the next generation of jet engine concepts, the current study aimed to originate a database of variable external flow with effective aerodynamic parameters, which have influence on fluidic thrust-Vector control.