Multiobjective mathematical programming problems, in particular the vector optimization problems, de ne a well known and studied area because of its relevance to numerous practical applications. In this paper vector optimization problems with a fuzzy nature are considered. In these problems usually it is assumed that all the objective functions involved come from the same decision maker. The pr...

There are many numerous methods for solving large-scale problems in which some of them are very flexible and efficient in both linear and non-linear cases. League championship algorithm is such algorithm which may be used in the mentioned problems. In the current paper, a new play-off approach will be adapted on league championship algorithm for solving large-scale problems. The proposed algori...

In this paper, we study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution ma...

We propose a nearest point algorithm (NPA) for optimization of a family of Support Vector Machines (SVM) methods. Geometrically, optimizing SVM corresponds to finding the nearest points between two polyhedrons. In classification, the hard margin case corresponds to finding the closest points of the convex hull of each class. The soft margin case corresponds to finding the closest points in the ...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

In a convex optimization problem, x ∈ R is a vector known as the optimization variable, f : R → R is a convex function that we want to minimize, and C ⊆ R is a convex set describing the set of feasible solutions. From a computational perspective, convex optimization problems are interesting in the sense that any locally optimal solution will always be guaranteed to be globally optimal. Over the...

Support vector machine is an elegant tool for solving pattern recognition and regression problems. This paper presents a new smooth approach to solve support vector regression. Based on statistical learning theory and optimization theory, a smooth unconstrained optimization model for support vector regression is built with adjustable entropy technique. Newton descent method is used to solve the...