Nonlinear Optimization, Nonsmooth Optimization, Classification Problems
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  a new strategy for tuning the proximity parameter has been devised, while a different method for managing the bundle information is given in . In  and , bundle methods have been extended to the nonconvex case: in particular, while in  a trust region approach is used for computing the search direction, in  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 ), the algorithm devised in  has been also adopted for solving TSVM (Transductive Support Vector Machine) problems .
In  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  and  two different approaches have been devised for solving, respectively, smooth constrained and unconstrained optimization problems, while in  and  two case studies of optimization in logistics have been faced.
 A. Astorino, A. Fuduli, M. Gaudioso. DC models for spherical separation. Journal of Global Optimization, 48(4), pp. 657--669, 2010.
 A. Astorino, A. Fuduli, E. Gorgone. Nonsmoothness in classification problems. Optimization Methods and Software, 23(5), pp. 675--688, 2008.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.  L. Chauvier, A. Fuduli, J.C. Gilbert. A truncated SQP algorithm for solving nonconvex equality constrained optimization problems
 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.
 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