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".

In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global optimal solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

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.

In this paper, we study approximate proper efficient (nondominated and minimal) solutions of Vector optimization problems with variable ordering structures (VOSs). In Vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondominated/ minimal solutions are defined in different senses (Henig, Benson, and Borwein) for problems with VOSs from new stand-points. The relationships among the introduced notions are studied, and some scalarization approaches are developed to characterize these solutions. These scalarization results based on new functionals defined by elements from the dual cones are given. Moreover, some existing results are ad-dressed.

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.