# Manlio GaudiosoUniversità della Calabria | Università della Calabria · Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica

Manlio Gaudioso

Laurea Degree in Electrical Engineering

## About

110

Publications

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Introduction

**Skills and Expertise**

## Publications

Publications (110)

Approximately sixty years ago two seminal findings, the cutting plane and the subgradient methods, radically changed the landscape of mathematical programming. They provided, for the first time, the practical chance to optimize real functions of several variables characterized by kinks, namely by discontinuities in their derivatives. Convex functio...

We present a fast heuristic approach for solving a binary multiple instance learning (MIL) problem, which consists in discriminating between two kinds of item sets: the sets are called bags and the items inside them are called instances. Assuming that only two classes of instances are allowed, a common standard hypothesis states that a bag is posit...

We consider polyhedral separation of sets as a possible tool in supervised classification. In particular, we focus on the optimization model introduced by Astorino and Gaudioso (J Optim Theory Appl 112(2):265–293, 2002) and adopt its reformulation in difference of convex (DC) form. We tackle the problem by adapting the algorithm for DC programming...

We consider the directional sensor network lifetime maximization problem (DSLMP). Given a set of directional sensor and target locations, the problem consists in assigning, at each time unit of a given time horizon, the action radius, the aperture angle, and the orientation direction to all sensors. The objective is to maximize the number of time u...

This article addresses the minimum spanning tree problem with conflicting edge pairs, a variant of the classical minimum spanning tree where, given a list of conflicting edges, the goal is to find the cheapest spanning tree with no edges in conflict. We adopt a Lagrangian relaxation approach together with a dual ascent and a subgradient procedure t...

We consider a multiple instance learning problem where the objective is the binary classifications of bags of instances, instead of single ones. We adopt spherical separation as a classification tool and come out with an optimization model which is of difference-of-convex type. We tackle the model by resorting to a specialized nonsmooth optimizatio...

Approximately 60 years ago two seminal findings, the cutting plane and the subgradient methods, radically changed the landscape of mathematical programming. They provided, for the first time, the practical chance to optimize real functions of several variables characterized by kinks, namely by discontinuities in their derivatives. Convex functions,...

The paper describes a Lagrangian heuristic algorithm for a cross-docking problem, where given amounts of several products must be directly transshipped from a given set of inbound trucks to a given set of outbound trucks. The cross-docking centre is equipped with some inbound and outbound doors (or gates), where the discharging/loading activities,...

We provide an introduction to Lagrangian relaxation, a methodology which consists in moving into the objective function, by means of appropriate multipliers, certain complicating constraints of integer programming problems. We focus, in particular, on the solution of the Lagrangian dual, a nonsmooth optimization (NSO) problem aimed at finding the b...

We treat the feature selection problem in the support vector machine (SVM) framework by adopting an optimization model based on use of the \(\ell _0\) pseudo-norm. The objective is to control the number of non-zero components of the normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the...

Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects...

This paper is motivated by the case of a forwarder dealing with inland transportation planning, from a seaport, of inbound containers filled with pallets having different destinations in the land‐side. Although the forwarder is not the owner nor controls any vehicle, he is required to plan both the assignment of containers to intermediate depots, w...

We present a new disaggregated formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator. This formulation consists of O(mnn) variables and constraints, where m denotes the number of concentrators and n the number of terminals, respectively. We prove that this extende...

In the standard classification problems, the objective is to categorize points into different classes. Multiple instance learning (MIL), instead, is aimed at classifying bags of points, each point being an instance. The main peculiarity of a MIL problem is that, in the learning phase, only the label of each bag is known whereas the labels of the in...

This book presents expert descriptions of the successful application of operations research in both the private and the public sector, including in logistics, transportation, product design, production planning and scheduling, and areas of social interest. Each chapter is based on fruitful collaboration between researchers and companies, and compan...

We introduce a methodology for operational planning of cooperation between two independent shippers who manage their own fleets of vehicles in a given geographic area. We assume that shippers are willing to establish partial cooperation by sharing only a subset of customers. Our approach is based on the iterative attempt of identifying subsets of s...

In binary Multiple Instance Learning (MIL) the objective is to discrimi-Sept. 11 th 16.30-18.30 Majorana nate between positive and negative sets of points. In the MIL terminology each set is called bag and the points inside each bag are called instances. In the case of two classes of instances (positive and negative), a bag is positive when it cont...

After a brief survey on well established methods for image classification, we focus on a recently proposed Multiple Istance Learning (MIL) method which is suitable for applications in image processing.
In particular the method is based on a mixed integer nonlinear formulation of the optimization problem to be solved for MIL purposes. The algorithm...

We introduce a proximal bundle method for the numerical minimization of a nonsmooth difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane approaches for the convex case, we iteratively build two separate piecewise-affine approximations of the component functions, grouping the corresponding information in two se...

We introduce an iterative method for solving linearly constrained optimization problems, whose nonsmooth nonconvex objective function is defined as the pointwise maximum of finitely many concave functions. Such problems often arise from reformulations of certain constraint structures (e.g., binary constraints, finite max-min constraints) in diverse...

We address the problem of synchronizing the loading and discharging operations of trucks at a particular cross-docking center, with one door at both the inbound and outbound sides, aiming at minimizing the makespan of the whole process. We propose a mixed integer linear model and a Lagrangian decomposition scheme. We derive conditions for optimally...

We consider the truck scheduling problem at a cross docking terminal with many inbound and outbound doors, under the assumption of constant handling time for all the trucks, the objective being to minimize the completion time of the whole process. We propose a mathematical model together with a Lagrangian Relaxation scheme. We discuss the structura...

We introduce and test a binary classification method aimed at detecting malicious URL on the basis of some information on both the URL syntax and its domain properties. Our method belongs to the class of supervised machine learning models, where, in particular, classification is performed by using information coming from a set of URL’s (samples in...

The link constrained Steiner tree problem is a variant of the classic Steiner tree problem where the number of links to be activated must not exceed a pre-fixed value. We introduce a multi-start heuristic to obtain a quick feasible solution. The proposed heuristic is embedded into a decomposition framework based on Lagrangean relaxation. In particu...

We describe an algorithm for minimizing convex, not necessarily smooth, functions of several variables, based on a descent direction finding procedure that inherits some characteristics both of standard bundle method and of Wolfe’s conjugate subgradient method. This is obtained by allowing appropriate upward shifting of the affine approximations of...

Nonsmooth optimization is traditionally based on convex analysis and most solution methods rely strongly on the convexity of the problem. In this paper, we propose an efficient diagonal bundle method for nonconvex large-scale nonsmooth optimization. The novelty of the new method is in different usage of metrics depending on the convex or concave be...

The objective of the paper is to evaluate the impact of the infinity computing paradigm on practical solution of nonsmooth unconstrained optimization problems, where the objective function is assumed to be convex and not necessarily differentiable. For such family of problems, the occurrence of discontinuities in the derivatives may result in failu...

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in the Support Vector Machine (SVM) framework for binary classification. In particular we embed into our objective function a weighted combination of the L1 and L0 norm of the normal to the separating hyperplane. We come out with a Mixed Binary Linear Programming...

We propose a robust spherical separation technique aimed at separating two finite sets of points
and
. Robustness concerns the possibility to admit uncertainties and perturbations in the data-set, which may occur when the data are corrupted by noise or are influenced by measurement errors. In particular, starting from the standard spherical separa...

We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the nor...

We present a mixed integer nonlinear programming formulation of the Directional Sensors Continuous Coverage Problem (DSCCP), where a given set of targets on a plane are to be covered by a set of sensors whose locations are known. Sensors are supposed to be directional, that is characterized by a discrete set of possible radii and aperture angles. T...

We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, cust...

The Directional Sensors Continuous Coverage Problem (DSCCP) aims at covering a given set of targets in a plane by means of a set of directional sensors. The location of these sensors is known in advance and they are characterized by a discrete set of possible radii and aperture angles. Decisions to be made are about orientation (which in our approa...

Let (Formula presented.) be a finite set in (Formula presented.). The illumination problem addressed in this work concerns the optimal location and orientation of a conic light beam (Formula presented.)The aperture angle (Formula presented.) of the conic light beam is a decreasing function of the sharpness coefficient (Formula presented.). The prob...

This paper addresses a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood set of that node. The problem is known as the close-enough traveling salesman problem. We introduce a new effective discretization scheme that allows us to compute both a lower and an upper bound for t...

We address a variant of the classical Steiner tree problem defined over undirected graphs. The objective is to determine the Steiner tree rooted at a source node with minimum cost and such that the number of edges is less than or equal to a given threshold. The link constrained Steiner tree problem (\(\mathcal {LCSTP}\)) belongs to the NP-hard clas...

We propose models and algorithms for two problems arising in the management of the Gioia Tauro maritime terminal in Southern Italy. Both problems are formulated as integer linear programs and solved by CPLEX for relatively small sizes. For larger instances we have developed highly efficient tabu search heuristics. These algorithms will be implement...

The separation problem of two sets, whose convex hulls have a nonempty intersection, is considered. In order to find a solution of the problem algorithms of local and global search are developed. The efficiency of the algorithms is demonstrated by computational simulations on test examples.

The genetic algorithm (GA) is a quite efficient paradigm to solve several optimization problems. It is substantially a search technique that uses an ever-changing neighborhood structure related to a population which evolves according to a number of genetic operators. In the GA framework many techniques have been devised to escape from a local optim...

We introduce a new notion of central axis for a finite set {a 1 ,. .. , a m } of vectors in R n. In tandem, we discuss different ways of measuring the dispersion of the data points a i 's around the central axis. Finally, we explain how to detect numerically the most peripheral points of the given dataset. Keywords Central axis of a dataset · Conic...

Professor Vladimir Fedorovich Demyanov from St. Petersburg State University passed away on April 18, 2014. He was born in Dniepropetrovsk in August 18, 1938. His whole life was linked to the University of Leningrad (now St. Petersburg). In 1960, he graduated from the University of Leningrad from the Department of Computational Mathematics organized...

We present a bundle method for solving convex semi-infinite minmax problems which allows inexact solution of the inner maximization. The method is of the partially inexact oracle type, and it is aimed at reducing the occurrence of null steps and at improving bundle handling with respect to existing methods.Termination of the algorithm is proved at...

In this paper we consider a generalization of the separation technique proposed in Gaudioso et al. (Optimization 59:1199–1210, 2011) and Grzybowski et al. (Optim. Methods Softw. 20:219–229, 2005) for the separation of finitely many compact convex sets A
i
, i ∈ I by another compact convex set S in a locally convex vector space. We construct separat...

Let
$\{a_i:i\in I\}$
be a finite set in
$\mathbb R ^n$
. The illumination problem addressed in this work is about selecting an apex
$z$
in a prescribed set
$Z\subseteq \mathbb R ^n$
and a unit vector
$y\in \mathbb R ^n$
so that the conic light beam
$$\begin{aligned} C(z,y,s):= \{x \in \mathbb R ^n : s\,\Vert x-z\Vert - \langle y, x-z\ra...

This work addresses the issue of separating two finite sets in ℝ n by means of a suitable revolution cone Γ(z,y,s)={x∈ℝ n :s∥x-z∥-y T (x-z)=0}· The specific challenge at hand is to determine the aperture coefficient s, the axis y, and the apex z of the cone. These parameters have to be selected in such a way as to meet certain optimal separation cr...

We present a bundle-type method for minimizing non-convex non-smooth functions. Our approach is based on the partition of the bundle into two sets, taking into account the local convex or concave behaviour of the objective function. Termination at a point satisfying an approximate stationarity condition is proved and numerical results are provided.

We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and compare different relaxations of them, namely Lagrangia...

We describe an optimization-based method for tackling the classic image
processing problem known as edge detection and we formulate it in the form of a
classification one. The novelty of the approach is in the use of spherical separation as
a classification tool in the image processing framework. Spherical separation consists
in separating bymeans...

Rising energy prices and customers’ increasing ecological awareness pushed energy efficient manufacturing to the top position
in industrial interests. Actually, companies want to identify the most effective measures to increase energy efficiency in
manufacturing processes looking at the sustainability of their product as a point of strength and not...

Import companies operating in the globalized market and in a multi-item context are frequently faced with the need of aggregating their orders to benefit from scale economies associated to the use of containers for freight shipping.
We introduce the problem of optimal replenishment order placement, namely the problem of scheduling and aggregating...

We face the problem of strictly separating two sets of points by means of a sphere, considering the two cases where the center of the sphere is fixed or free, respectively. In particular, for the former we present a fast and simple solution algorithm, whereas for the latter one we use the DC-Algorithm based on a DC decomposition of the error functi...

We present a bundle method for convex nondifferentiable minimization where the model is a piecewise quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from below at a properly chosen (small) subset of points, as opposed to everywhere. We provide the con...

The literature in the area of the semi-supervised binary classification has demonstrated that useful information can be gathered not only from those samples whose class membership is known in advance, but also from the unlabelled ones. In fact, in the support vector machine, semi-supervised models with both labelled and unlabelled samples contribut...

We propose two different approaches for spherical separation of two sets. Both methods are based on minimizing appropriate
nonconvex nondifferentiable error functions, which can be both expressed in a DC (Difference of two Convex) form. We tackle
the problem by adopting the DC-Algorithm. Some numerical results on classical binary datasets are repor...

In this article we consider a separation technique proposed in J. Grzybowski, D. Pallaschke, and R. Urbański (A pre-classification and the separation law for closed bounded convex sets, Optim. Method Softw. 20(2005), pp. 219–229) for separating two convex sets A and B with another convex set C. We prove that in a finite dimension C can be chosen as...

Although the competitiveness of the Incremental Sheet Forming process is deeply assessed, some specific aspects penalise its
industrial application. In particular, the idea to take advantage of the bigger formability appears of a great interest but
the non homogeneous thickness distribution reduces the industrial applicability. It is well known tha...

Standard assignment is the problem of obtaining a matching between two sets of respectively persons and positions so that
each person is assigned exactly one position and each position receives exactly one person, while a linear decision maker
utility function is maximized. We introduce a variant of the problem where the persons individual utiliti...

We present a numerical bundle-type method for local minimization of a real function of several variables, which is supposed to be locally Lipschitz.We provide a short survey of some optimization algorithms from the literature, which are able to deal with both nonsmoothness and nonconvexity of the objective function. We focus on possible extensions...

The Lagrangian dual of an integer program can be formulated as a min-max problem where the objective function is convex, piecewise affine and, hence, nonsmooth. It is usually tackled by means of subgradient algorithms, or multiplier adjustment techniques, or even more sophisticated nonsmooth optimization methods such as bundle-type algorithms.
Rece...

We consider a special case of the optimal separation, via a sphere, of two discrete point sets in a finite dimensional Euclidean
space. In fact we assume that the center of the sphere is fixed. In this case the problem reduces to the minimization of a
convex and nonsmooth function of just one variable, which can be solved by means of an “ad hoc” me...

We present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables. The algorithm is
based on the construction of both a lower and an upper polyhedral approximation of the objective function. In particular,
at each iteration, a search direction is computed by solving a quadratic program aiming at maximizing th...

We describe an Electronic Nose (ENose) system which is able to identify the type of analyte and to estimate its concentration. The system consists of seven sensors, five of them being gas sensors (supplied with different heater voltage values), the remainder being a temperature and a humidity sensor, respectively. To identify a new analyte sample a...

We present an Electronic Nose (ENose), which is aimed at identifying the presence of one out of two gases, possibly detecting the presence of a mixture of the two. Estimation of the concentrations of the components is also performed for a volatile organic compound (VOC) constituted by methanol and acetone, for the ranges 40-400 and 22-220 ppm (part...

We present an Electronic Nose (ENose) which is aimed both at identifying the type of gas and at estimating its concentration. Our system contains 8 sensors, 5 of them being gas sensors (of the class TGS from FIGARO USA, INC., whose sensing element is a tin dioxide (SnOz) semiconductor), the remaining being a temperature sensor (LM35 from National S...

The Service Allocation Problem (SAP) is a tactical problem arising in the yard management of a container transshipment terminal. The objective is the minimization of the container rehandling operations inside the yard. This study of the SAP was undertaken for the Gioia Tauro port which is located in Italy and is the main hub terminal for container...

We present a new bundle method in which the use of the proximal trajectory of the cutting plane function allows the automatic
tuning of the proximity parameter. An updating criterion of the stability center based on the agreement between the objective
function and the polyhedral model is presented. Convergence properties are provided together with...