Gerardo Toraldo

High Performance Algorithms and Software in Nonlinear Optimization

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSNO97) which was held in Ischia, Italy, in June, 1997. The book provides an overview of the nonlinear optimization field, including algorithms, software evaluation, implementation issues, applications, and areas of research, through authoritative papers by some of the most active and well-known researchers in the field. The papers of the Proceedings can be recommended to mathematicians, physicists, and engineers working in the fields mentioned above, as well as recommended for further reading within graduate studies.

Quadratic Programming with Box Constraints

The global minimization of quadratic problems with box constraints naturally arises in many applications and as a subproblem of more complex optimization problems. In this paper we briefly describe the main results on global optimality conditions. Moreover, some of the most interesting computational approaches for the problem will be summarized.

Ellipsoidal Approach to Box-Constrained Quadratic Problems

We present a new heuristic for the global solution of box constrained quadratic problems, based on the classical results which hold for the minimization of quadratic problems with ellipsoidal constraints. The approach is tested on several problems randomly generated and on graph instances from the DIMACS challenge, medium size instances of the Maximum Clique Problem. The numerical results seem to suggest some effectiveness of the proposed approach.

On the identification property of a projected gradient method

The authors study the convergence properties of a projected gradient algorithm for the general problem \[\min \{ f(x):x \in \Omega \} ,\] where

On the steplength selection in gradient methods for unconstrained optimization

f:R^n \to R

A Parallel Implementation of a Potential Reduction Algorithm for Box-Constrained Quadratic Programming

is a mapping continuously differentiable on a closed convex set

A generalized eigenvalues classifier with embedded feature selection

\Omega \subseteq R^n

A note on spectral properties of some gradient methods

.The algorithm, which requires only one projection per iteration, is a special version of the method of projection of the gradient by Demyanov and Rubinov [Approximate Methods in Optimization Problems, Elsevier, New York, 1970] where the step choice is made according to a scheme similar to the one used by Calamai and More [Math. Programming, 39 (1987), pp. 93–116]. The authors are mainly interested in analysing the identification property of the algorithm for the case where the set

An adaptable learning technology system for mathematical models

\Omega

A predictive Decision Support System (DSS) for a microalgae production plant based on Internet of Things paradigm

is a polyhedron, that is, the ability to identify in a finite number of steps the face in which the final solution lies.The convergence results that are shown are very similar to those shown in [6] for the standard projected gradient method.