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.

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 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.

The primary objective of this research is toobtain an accurate forecasting model for the US presidentialelection. To identify a reliable model, artificial neuralnetworks (ANN) and support Vector regression (SVR)models are compared based on some specified performancemeasures. Moreover, six independent variables such asGDP, unemployment rate, the president’ s approval rate, and others are considered in a stepwise regression toidentify significant variables. The president’ s approval rateis identified as the most significant variable, based onwhich eight other variables are identified and considered inthe model development. Preprocessing methods are appliedto prepare the data for the learning algorithms. The proposedprocedure significantly increases the accuracy of themodel by 50%. The learning algorithms (ANN and SVR)proved to be superior to linear regression based on eachmethod’ s calculated performance measures. The SVRmodel is identified as the most accurate model among theother models as this model successfully predicted theoutcome of the election in the last three elections (2004, 2008, and 2012). The proposed approach significantlyincreases the accuracy of the forecast.

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".

Facility location problem (FLP) is a mathematicalway to optimally locate facilities within a set of candidatesto satisfy the requirements of a given set of clients. This study addressed the uncapacitated FLP as it assuresthat the capacity of every selected facility is finite. Thus, even if the demand is not known, which often is the case, inreality, organizations may still be able to take strategicdecisions such as locating the facilities. There are differentapproaches relevant to the uncapacitated FLP. Here, thecuckoo search via Le´ vy flight (CS-LF) was used to solvethe problem. Though hybrid methods produce betterresults, this study employed CS-LF to determine first itspotential in finding solutions for the problem, particularlywhen applied to a real-world problem. The method wasapplied to the data set obtained from a department store inDavao City, Philippines. Results showed that applying CSLFyielded better facility locations compared to particleswarm optimization and other existing algorithms. Although these results showed that CS-LF is a promisingmethod to solve this particular problem, further studies onother FLP are recommended to establish a strong foundationof the capability of CS-LF in solving FLP.

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.