We consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given and some results on duality are proved. Mathematics Subject Classifications. 90C46, 49K27, 93C25.

Our goal in this talk is to present unifying concepts for both stochastic and robust optimization problems involving infinite uncertainty sets. We apply methods from vector optimization in general spaces, set-valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming. These methods provide new in...

In this paper we consider a vector optimization problem; we present some scalarization techniques for finding all the vector optimal points of this problem and we discuss the relationships between these methods. Moreover, in the linear case, the study of dual variables is carried on by means of sensitivity analysis and also by a parametric approach. We also give an interpretation of the dual va...

Considerable efforts have been devoted to the implementation of efficient optimization method for solving the Support Vector Machine dual problem. This document proposes an historical perspective and and in depth review of the algorithmic and computational issues associated with this problem.

In classification problems classes usually have different geometrical structure and therefore it seems natural for each class to have its own margin type. Existing methods using this principle lead to the construction of the different (from SVM) optimization problems. Although they outperform the standard model, they also prevent the utilization of existing SVM libraries. We propose an approach...

Chimp Optimization Algorithm (ChOA), a novel meta-heuristic algorithm, has been proposed in recent years. It divides the population into four different levels for purpose of hunting. However, there are still some defects that lead to algorithm falling local optimum. To overcome these defects, an Enhanced (EChOA) is developed this paper. Highly Disruptive Polynomial Mutation (HDPM) introduced fu...

The binary support vector machines (SVMs) have been extensively investigated. However their extension to a multi-classification model is still an on-going research. In this paper we present an extension of the binary support vector machines (SVMs) for the k > 2 class problems. The SVM model as originally proposed requires the construction of several binary SVM classifiers to solve the multi-cla...

We propose a new formulation for the optimal separation problems. This robust formulation is based on finding the minimum volume ellipsoid covering the points belong to the class. Idea is to separate by ellipsoids in the input space without mapping data to a high dimensional feature space unlike Support Vector Machines. Thus the distance order in the input space is preserved. Hopfield Neural Ne...