## Academic Staff

### Antonio Fuduli

Email: antonio.fuduli[AT]unical.it

Personal site

**Expertise**:

Nonlinear Optimization, Nonsmooth Optimization, Classification Problems

**Research**:

The main research activity is on Nonsmooth Optimization, with particular emphasis to bundle methods for the minimization of convex [4, 6, 12] and nonconvex functions [7, 8].

Bundle methods have been initially conceived for minimizing convex nondifferentiable functions. They are based on the construction of a polyhedral model approximating from below the objective function. Such a model is obtained on the basis of a bundle of points computed at the previous iterations. The search direction is calculated by solving a quadratic program whose the objective function is given by the weighted sum of two conflictive objectives: on one hand we want to minimize the polyhedral model and on the other hand we want to minimize the Euclidean distance between the new point and the current point. A positive parameter, named the proximity parameter, is aimed at trading off between the two objectives and its tuning is fundamental for convergence reasons.

In [6] a new strategy for tuning the proximity parameter has been devised, while a different method for managing the bundle information is given in [4]. In [7] and [8], bundle methods have been extended to the nonconvex case: in particular, while in [7] a trust region approach is used for computing the search direction, in [8] a DC (Difference of Convex functions) polyhedral model is adopted. Moreover, since most of optimization problems arising in machine learning are of nonsmooth nature (see [2]), the algorithm devised in [7] has been also adopted for solving TSVM (Transductive Support Vector Machine) problems [3].

In [1] the problem of separation of sets by means of a sphere has been faced by DCA (DC-Algorithm) techniques. In such case in fact the nonsmooth classification error function can be easily put in the form of DC function.

In [9] and [11] two different approaches have been devised for solving, respectively, smooth constrained and unconstrained optimization problems, while in [5] and [10] two case studies of optimization in logistics have been faced.

REFERENCES:

[1] A. Astorino, A. Fuduli, M. Gaudioso. DC models for spherical separation. Journal of Global Optimization, 48(4), pp. 657--669, 2010.

[2] A. Astorino, A. Fuduli, E. Gorgone. Nonsmoothness in classification problems. Optimization Methods and Software, 23(5), pp. 675--688, 2008.

[3] A. Astorino, A. Fuduli. Nonsmooth optimization techniques for semi--supervised classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(12), pp. 2135--2142, 2007.

[4] A.V. Demyanov, A. Fuduli, G. Miglionico. A bundle modification strategy for convex minimization. European Journal of Operational Research, 180(1), pp. 38--47, 2007.

[5] A. Attanasio, A. Fuduli, G. Ghiani. C. Triki. Integrated shipment dispatching and packing problems: a case study. Journal of Mathematical Modelling and Algorithms, 6(1), pp. 77--85, 2007.

[6] A. Fuduli, M. Gaudioso. Tuning strategy for the proximity parameter in convex minimization. Journal of Optimization Theory and Applications, 130(1), pp. 95--112, 2006.

[7] A. Fuduli, M. Gaudioso, G. Giallombardo. Minimizing nonconvex nonsmooth functions via cutting planes and proximity control. SIAM Journal on Optimization, 14(3), pp. 743-756, 2004.

[8] A. Fuduli, M. Gaudioso, G. Giallombardo. A DC piecewise affine model and bundling technique in nonconvex nonsmooth minimization. Optimization Methods and Software, 19(1), pp. 89-102, 2004.

[9] M. Al-Baali, A. Fuduli, R. Musmanno. On the performance of switching BFGS/SR1 algorithms for unconstrained optimization. Optimization Methods and Software}, 19(2), pp. 153-164, 2004.

[10] A. Fuduli, A. Grieco, R. Musmanno, M. Ramundo. A three-stage load balancing model in a manufacturing company*. Journal of Information and Optimization Sciences, 25(1), pp. 177-187, 2004. *

*[11] L. Chauvier, A. Fuduli, J.C. Gilbert. A truncated SQP algorithm for solving nonconvex equality constrained optimization problems*. In G. Di Pillo and A. Murli (Eds), High Performance Algorithms and Software for Nonlinear Optimization, pp. 149-176, Kluwer Academic Publishers B.V. - 2003.

[12] A. Fuduli, M. Gaudioso. Fixed and virtual stability center methods for convex nonsmooth minimization*. In G. Di Pillo and F. Giannessi (Eds), Nonlinear Optimization and Related Topics, pp. 105-122, Kluwer Academic Publishers B.V. - 2000 *