Design of induction motors using a mixed-variable approach

In this paper we are concerned with the problem of optimally designing three-phase induction motors. This problem can be formulated as a mixed variable programming problem. Two different solution strategies have been used to solve this problem. The first one consists in solving the continuous nonlinear optimization problem obtained by suitably relaxing the discrete variables. On the opposite, the second strategy tries to manage directly the discrete variables by alternating a continuous search phase and a discrete search phase. The comparison between the numerical results obtained with the above two strategies clearly shows the fruitfulness of taking directly into account the presence of both continuous and discrete variables.This work was supported by CNR/MIUR Research Program “Metodi e sistemi di supporto alle decisioni”, Rome, Italy.     

Characterizations of α-Bloch spaces on the unit ball

We obtain a characterization of the α-Bloch space for any α>0 in the unit ball of Cn in terms of |f(z)−f(w)|/|z−w|. Moreover, a new characterization for the Bloch space is given.     

The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions

In this paper, a new nonmonotone MBFGS algorithm for unconstrained optimization will be proposed. Under some suitable assumptions, the global and superlinear convergence of the new nonmonotone MBFGS algorithm on convex objective functions will be established. Some numerical experiments show that this new nonmonotone MBFGS algorithm is competitive to the MBFGS algorithm and the nonmonotone BFGS algorithm.     

A Combined Global & Local Search (CGLS) Approach to Global Optimization

This paper presents a general approach that combines global search strategies with local search and attempts to find a global minimum of a real valued function of n variables. It assumes that derivative information is unreliable; consequently, it deals with derivative free algorithms, but derivative information can be easily incorporated. This paper presents a nonmonotone derivative free algorithm and shows numerically that it may converge to a better minimum starting from a local nonglobal minimum. This property is then incorporated into a random population to globalize the algorithm. Convergence to a zero order stationary point is established for nonsmooth convex functions, and convergence to a first order stationary point is established for strictly differentiable functions. Preliminary numerical results are encouraging. A Java implementation that can be run directly from the Web allows the interested reader to get a better insight of the performance of the algorithm on several standard functions. The general framework proposed here, allows the user to incorporate variants of well known global search strategies. Research done under the cooperation agreement between Universidade de Vigo and Universidad Simón Bolívar.     

Multidimensional Lipschitz global optimization based on efficient diagonal partitions

This is a summary of the author’s PhD thesis, supervised by Yaroslav D. Sergeyev and defended on May 5, 2006, at the University of Rome “La Sapienza”. The thesis is written in English and is available from the author upon request. In this work, the global optimization problem of a multidimensional “black-box” function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. The objective function is assumed hard to evaluate. A new efficient diagonal scheme for constructing fast algorithms for solving this problem is examined and illustrated by developing several powerful global optimization methods. A deep theoretical study is performed which highlights the benefit of the approach introduced over traditionally used diagonal algorithms. Theoretical conclusions are confirmed by results of extensive numerical experiments.      

A generating set search method using curvature information

Direct search methods have been an area of active research in recent years. On many real-world problems involving computationally expensive and often noisy functions, they are one of the few applicable alternatives. However, although these methods are usually easy to implement, robust and provably convergent in many cases, they suffer from a slow rate of convergence. Usually these methods do not take the local topography of the objective function into account. We present a new algorithm for unconstrained optimisation which is a modification to a basic generating set search method. The new algorithm tries to adapt its search directions to the local topography by accumulating curvature information about the objective function as the search progresses. The curvature information is accumulated over a region thus smoothing out noise and minor discontinuities. We present some theory regarding its properties, as well as numerical results. Preliminary numerical testing shows that the new algorithm outperforms the basic method most of the time, sometimes by significant relative margins, on noisy as well as smooth problems. This work was supported by the Norwegian Research Council (NFR).     

Outdoor WLAN planning via non-monotone derivative-free optimization: algorithm adaptation and case study

In this paper, we study the application of non-monotone derivative-free optimization algorithms to wireless local area networks (WLAN) planning, which can be modeled as an unconstrained minimization problem. We wish to determine the access point (AP) positions that maximize coverage in order to provide connectivity to static and mobile users. As the objective function of the optimization model is not everywhere differentiable, previous research has discarded gradient methods and employed heuristics such as neighborhood search (NS) and simulated annealing (SA). In this paper, we show that the model fulfills the conditions required by recently proposed non-monotone derivative-free (DF) algorithms. Unlike SA, DF has guaranteed convergence. The numerical tests reveal that a tailored DF implementation (termed “zone search”) outperforms NS and SA. A collaboration between U. of Vigo, Spain and USB, Venezuela.     

Derivative free optimization methods for optimizing stirrer configurations

In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier–Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids, for allowing a flexible discretization of complex stirrer geometries. Two derivative free optimization algorithms, the DFO and CONDOR are considered, they are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. Both are designed to minimize smooth functions whose evaluations are considered to be expensive and whose derivatives are not available or not desirable to approximate. An exemplary application for a standard stirrer configuration illustrates the functionality and the properties of the proposed methods. It also gives a comparison of the two optimization algorithms.     

Variants of Steffensen-secant method and applications

In this paper, a parametric variant of Steffensen-secant method and three fast variants of Steffensen-secant method for solving nonlinear equations are suggested. They achieve cubic convergence or super cubic convergence for finding simple roots by only using three evaluations of the function per step. Their error equations and asymptotic convergence constants are deduced. Modified Steffensen’s method and modified parametric variant of Steffensen-secant method for finding multiple roots are also discussed. In the numerical examples, the suggested methods are supported by the solution of nonlinear equations and systems of nonlinear equations, and the application in the multiple shooting method.     

Local Optimization Method with Global Multidimensional Search

This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithms allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima.