Support Vector Machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. Nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we will present the convex...

High performance computing (HPC) technology, including parallel and/or vector processing, provides opportunities to solve process optimization and simulation problems faster and more reliably than ever before, thus enabling the solution of increasingly large scale problems, even in a real time environment. This presentation will focus on recent advances in HPC technology and methods for exploit...

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on φ-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization ...

In this paper, we consider different kinds of generalized invexity for vector valued functions and a vector optimization problem. Some relations between some vector variational-like inequalities and a vector optimization problem are established using the properties of Mordukhovich limiting subdifferentials under C − η−strong pseudomonotonicity. Mathematics Subject Classification (2010): 26A51, ...

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemann...

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...

This paper introduces a modification on the movement force vector of the Birbil and Fang’s electromagnetism-like algorithm [1] for solving global optimization problems with bounded variables. The proposed movement vector combines the total force exerted on each point of the population, at the current iteration, with the rate of change in the force vector of a previous iteration. Several widely ...

The execution process of the queries in distributed databases require accurate estimations and predictions for performance characteristics. The problems of data allocation and query optimization done by means of mobile agents and evolutionary algorithms are considered. These problems still present a challenge because of the dynamic changes in number of components and architectural complexity of...

Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds...