Stefano Lucidi

• full professor
• Sapienza University of Rome

This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We consider a derivative-free algorithm based on a linesearch extrapolation technique. First we prove that it enjoys the same complexity properties which have been proved f...

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit derivative information when possible in these scenarios: concretely, we propose an algorithmic framework that c...

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been...

In this paper we propose an heuristic to improve the performances of the recently proposed derivative-free method for nonsmooth optimization CS-DFN. The heuristic is based on a clustering-type technique to compute an estimate of Clarke’s generalized gradient of the objective function, obtained via calculation of the (approximate) directional deriva...

The combination of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) offers an unparalleled opportunity to study cortical physiology by characterizing brain electrical responses to external perturbation, called transcranial-evoked potentials (TEPs). Although these reflect cortical post-synaptic potentials, they can be contami...

This paper deals with the problem of cruise itinerary planning which plays a central role in worldwide cruise ship tourism. In particular, the Day-by-day Cruise Itinerary Optimization (DCIO) problem is considered. Assuming that a cruise has been planned in terms of homeports and journey duration, the DCIO problem consists in determining the daily s...

In this paper we propose an heuristic to improve the performances of the recently proposed derivative-free method for nonsmooth optimization CS-DFN. The heuristic is based on a clustering-type technique to compute a direction { which relies on an estimate of Clarke's generalized gradient} of the objective function. As such, this direction (as it is...

This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We prove that two linesearch-type algorithms enjoy the same complexity properties which have been proved for pattern and direct search algorithms. In particular, we conside...

The $$\ell _1$$ ℓ 1 -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the $$\ell _1$$ ℓ 1 -ball and embed it into...

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an...

In this paper, we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective function is costly or the objective function values are affected by some noise. These functionals have been r...

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature. Here, we propose to modify one of these algorithms, namely ALGENCAN by Andreani et al., in such a way to inco...

In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. Fi...

In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. Furthermore, we consider the case where a subset of the variables can only take integer values. We propose a new l...

Accurate modeling of the patient flow within an Emergency Department (ED) is required by all studies dealing with the increasing and well-known problem of overcrowding. Since Discrete Event Simulation (DES) models are often adopted with the aim of assessing solutions for reducing the impact of this worldwide phenomenon, an accurate estimation of th...

Disease gene prediction is to date one of the main computational challenges of precision medicine. It is still uncertain if disease genes have unique functional properties that distinguish them from other non-disease genes or, from a network perspective, if they are located randomly in the interactome or show specific patterns in the network topolo...

In the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make p...

In this paper we consider constrained optimization problems where both the objective and constraint functions are of the black-box type. Furthermore, we assume that the nonlinear inequality constraints are non-relaxable, i.e. their values and that of the objective function cannot be computed outside of the feasible region. This situation happens fr...

The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic sche...

A trading strategy simply consists in a procedure which defines conditions for buying or selling a security on a financial market. These decisions rely on the values of some indicators that, in turn, affect the tuning of the strategy parameters. The choice of these parameters significantly affects the performance of the trading strategy. In this wo...

In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative information) and we propose a new derivative-free linesearch-based algorithmic framework to suitably handle th...

Training a large multilayer neural network can present many difficulties due to the large number of useless stationary points. These points usually attract the minimization algorithm used during the training phase, which therefore results inefficient. Extending some results proposed in literature for shallow networks, we propose the mathematical ch...

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective function is costly or the objective function values are affected by some noise. These functionals have been co...

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature. Here, we propose to modify one of these algorithms, namely ALGENCAN [Andreani et al., 2007, Andreani et al.,...

Modeling the arrival process to an Emergency Department (ED) is the first step of all studies dealing with the patient flow within the ED. Many of them focus on the increasing phenomenon of ED overcrowding, which is afflicting hospitals all over the world. Since Discrete Event Simulation models are often adopted to assess solutions for reducing the...

The paper presents a multi-fidelity coordinate-search derivative-free algorithm for non-smooth constrained optimization (MF-CS-DFN), in the context of simulation-based design optimization (SBDO). The objective of the work is the development of an optimization algorithm able to improve the convergence speed of the SBDO process. The proposed algorith...

In this paper we consider the classical unconstrained nonlinear multiobjective optimization problem. For such a problem, it is particularly interesting to compute as many points as possible in an effort to approximate the so-called Pareto front. Consequently, to solve the problem we define an “a posteriori” algorithm whose generic iterate is repres...

In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfyin...

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an...

In this paper, we develop a new algorithmic framework to solve black-box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. Firs...

In this paper, a new derivative-free method for Worst Case Analysis (WCA) of circuit design is defined. A WCA of a device can be performed by solving a particular minimization problem where the objective function values are obtained by a simulation code and where some variables are subject to a spherical constraint and others to box constraints. In...

The aim of this paper is to optimize the design of multiple flux barriers Synchronous Reluctance Motor in order to smooth the torque profile without rotor skewing. A new strategy is proposed by modelling the particular optimal design problem as mixed integer constrained minimization of a suitable objective function. The procedure has allowed to opt...

In this data article, we report data and experiments related to the research article entitled “A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization”, by Cristofari et al. (2017). The method proposed in Cristofari et al. (2017), tackles optimization problems with bound constraints by properly combining an active-set estimate with a tr...

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we...

In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the last years. First we show that, given any stationary point that is not a global solution, it is possible to co...

The aim of this paper is to optimize the design of multiple flux barriers Synchronous reluctance motor in order to smooth the torque profile without rotor skewing. A new strategy is proposed by modelling the particular optimal design problem as mixed integer constrained minimization of a suitable objective function. The procedure has allowed to opt...

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) lineasearch method. Six MODHA formul...

In the field of global optimization, many efforts have been devoted to globally solving bound constrained optimization problems without using derivatives. In this paper we consider global optimization problems where both bound and general nonlinear constraints are present. To solve this problem we propose the combined use of a DIRECT-type algorithm...

Hospitals are huge and complex systems. However, for many years, the management was commonly focused on improving the quality of the medical care, while less attention was usually devoted to operation management. In recent years, the need of containing the costs while increasing the competitiveness along with the new policies of National Health Ser...

This paper deals with sales forecasting of a given commodity in a retail store of large distribution. For many years statistical methods such as ARIMA and Exponential Smoothing have been used to this aim. However the statistical methods could fail if high irregularity of sales are present, as happens for instance in case of promotions, because they...

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search framework recently proposed in [De Santis et al., 2012]. In the first stage, the algorithm exploits a property of th...

Simulation-based design optimization methods integrate computer simulations, design modification tools, and optimization algorithms. In hydrodynamic applications, often ob- jective functions are computationally expensive and noisy, their derivatives are not directly provided, and the existence of local minima cannot be excluded a priori, which moti...

A greedy randomized adaptive search procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solut...

The application of global/local hybrid DIRECT algorithms to the simulation-based hull form optimization of a military vessel is presented, aimed at the reduction of the resistance in calm water. The specific features of the black-box-type objective function make the problem suitable for the application of DIRECT-type algorithms. The objective funct...

In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points....

We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic i...

Hospitals have been challenged in recent years to deliver high quality care with limited resources. Given the pressure to contain costs, developing procedures for optimal resource allocation becomes more and more critical in this context. Indeed, under/overutilization of emergency room and ward resources can either compromise a hospital’s ability t...

A derivative-free global design optimization of the DTMB 5415 model is presented, using local hybridizations of two global algorithms, DIRECT (DIviding RECTangles) and PSO (Particle Swarm Optimization). The optimization aims at the reduction of the calm-water resistance at Fr = 0.25, using six design variables modifying hull and sonar dome. Simulat...

In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems the DIRECT algorithm has been proposed which has a good ability to locate promising regions of the feasible domain and convergence pro...

In this chapter we deal with global optimization problems where the objective function is computed by means of a possibly expensive simulation code. We present four real world challenging applications arising in different fields and describe four solution approaches that have been successfully applied to these applications. These solution algorithm...

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analys...

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several real-world problems (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the $\ell_1$-regularized least-squares approach that has been recently attracting the attenti...

Methods which do not use any derivative information are becoming popular among researchers, since they allow to solve many real-world engineering problems. Such problems are frequently characterized by the presence of discrete variables, which can further complicate the optimization process. In this paper, we propose derivative-free algorithms for...

In this paper, we propose new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence toward stationary points, using the Clarke--Jahn directional deri...

The identification of cell cycle-regulated genes through the cyclicity of mRNAs in genome-wide studies is a difficult task due to the presence of internal and external noise in microarray data. Moreover, the analysis is also complicated by the loss of synchrony occurring in cell cycle experiments, which often results in additional background noise....

In this paper, we introduce a framework for derivative-free robust optimization based on the use of an efficient derivative-free optimization routine for mixed-integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC–DC converter commonly used in portable electron...

Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty function for given values of the penalty parameter, and an au...

In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed integer problems.

Finding a feasible solution to a MIP problem is a tough task that has received much attention in the last decades. The Feasibility Pump (FP) is a heuristic for finding feasible solutions to MIP problems that has encountered a lot of success as it is very efficient also when dealing with very difficult instances. In this work, we show that the FP he...

Introduzione. L'ospedale è un sistema costoso e complesso, soggetto ad emergenze organizzative, la cui efficienza richiede scelte che tengano conto di svariati fattori, spesso in contrasto, e difficilmente armonizzabili con le necessità cliniche ed economiche dell'alta direzione Obiettivi. Uno degli obiettivi principali del progetto BuS-4H (progett...

Introduzione Il blocco operatorio costituisce un punto focale dell'attività di un'azienda ospedaliera: il suo ruolo è fondamentale sia da un punto di vista economico (in termini di costi e ricavi) che organizzativo. L'estrema complessità dell'attività chirurgica deriva dalle molteplici tipologie di intervento differenti sia per tempi di effettuazio...

In this paper we investigate the estimation problem for a model of the commodity prices. This model is a stochastic state space dynamical model and the problem unknowns are the state variables and the system parameters. Data are represented by the commodity spot prices, very seldom time series of Futures contracts are available for free. Both the s...

In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a non-differe...

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integ...

We are concerned with the solution of the bound constrained minimization problem {minf(x), l≤x≤u}. For the solution of this problem we propose an active set method that combines ideas from projected and nonmonotone Newton-type methods. It is based on an iteration of the form x k+1=[x k +α k d k ]♯, where α k is the steplength, d k is the search dir...

This paper proposes the design optimization procedure of three-phase interior permanent magnet (IPM) synchronous motors with minimum weight, maximum power output, and suitability for wide constant-power region operation. The particular rotor geometry of the IPM synchronous motor and the presence of several variables and constraints make the design...

Mixed-Integer optimization is a powerful tool for modeling many optimization problems arising from real-world applications. Finding a rst feasible solution represents the rst step for several MIP solvers. The Feasibility pump is a heuristic for nding feasible solutions to mixed integer linear problems which is eective even when dealing with hard MI...

OBIETTIVI: BAS (Business Administration Simulator) è un progetto per lo sviluppo sperimentale di un sistema a supporto della clincal governance di una azienda sanitaria. In particolare, nel 2011, lo studio ha riguardato la realizzazione di funzioni del sistema che permettessero di determinare case mix sostenibili per le attività di ricovero di una...

We propose a primal-dual algorithm for the solution of inequality constrained optimization problems. The distinguishing feature of the proposed algorithm is that of exploiting as much as possible the local non-convexity of the problem to the aim of producing a sequence of points converging to second order stationary points. In the unconstrained cas...

In this work, we study continuous reformulations of zero-one programming problems. We prove that, under suitable conditions, the optimal solutions of a zero-one programming problem can be obtained by solving a specific continuous problem.

Nonlinear programming problems with equality constraints and bound constraints on the variables are considered. The presence of bound constraints in the definition of the problem is exploited as much as possible. To this aim, an efficient search direction is defined which is able to produce a locally and superlinearly convergent algorithm and that...

The paper proposes an optimization procedure for the design of a three-phase Interior Permanent Magnet synchronous motor. The aim is to investigate the possibilities to maintain constant the power in the field-weakening region minimizing the active volume and maximizing the power output. The design optimization is based on a new algorithm belonging...

This paper is devoted to the study of partition-based deterministic algorithms for global optimization of Lipschitz-continuous functions without requiring knowledge of the Lipschitz constant. First we introduce a general scheme of a partition-based algorithm. Then, we focus on the selection strategy in such a way to exploit the information on the o...

In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty for...

In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally c...

In this paper we propose a new algorithm for solving difficult large-scale global optimization problems. We draw our inspiration from the well-known DIRECT algorithm which, by exploiting the objective function behavior, produces a set of points that tries to cover the most interesting regions of the feasible set. Unfortunately, it is well-known tha...

We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor explicitly approximated. Hence, every minimization procedure must use only a suitable sam...

The aim of this paper is to solve optimal design problems for industrial applications when the objective function value requires the evaluation of expensive simulation codes and its first derivatives are not available. In order to achieve this goal we propose two new algorithms that draw inspiration from two existing approaches: a filled function b...

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suit...

Training of support vector machines (SVMs) requires to solve a linearly constrained convex quadratic problem. In real applications, the number of training data may be very huge and the Hessian matrix cannot be stored. In order to take into account this issue, a common strategy consists in using decomposition algorithms which at each iteration opera...

Many real applications can be formulated as nonlinear minimization problems with a single linear equality constraint and box constraints. We are interested in solving problems where the number of variables is so huge that basic operations, such as the evaluation of the objective function or the updating of its gradient, are very time consuming. Thu...

In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth exact penalty f...

Recently a new derivative-free algorithm has been proposed for the solution of linearly constrained finite minimax problems. This derivative-free algorithm is based on a smoothing technique that allows one to take into account the non-smoothness of the max function. In this paper, we investigate, both from a theoretical and computational point of v...

In this work we consider nonlinear minimization problems with a single linear equality constraint and box constraints. In particular we are interested in solving problems where the number of variables is so huge that traditional optimization methods cannot be directly applied. Many interesting real world problems lead to the solution of large scale...

S. Lucidi, F. Rochetich and M. Roma [‘Curvilinear stabilization results for truncated Newton methods in large scale unconstrained optimization: the complete results’, Tech. Report 02.95, Dip. di Informatica e Sistemistica, Univ. di Roma “La Sapienza” (1995)] proposed recently a very general class of truncated Newton methods for solving large scale...

In this paper we define globally convergent algorithms for the solution of large dimensional unconstrained minimization problems. The algorithms proposed employ a nonmonotone steplength selection rule along the search direction which is determined by means of a Truncated-Newton algorithm. Numerical results obtained for a set of test problems are re...

Support Vector Machines (SVM) is a widely adopted technique both for classification and regression problems. Training of SVM requires to solve a linearly constrained convex quadratic problem. In real applications the number of training data may be very huge and the Hessian matrix can-not be stored. In order to take into account this issue a common...

In this paper conjugate gradient methods with nonmonotone line search technique are introduced. This new line search technique is based on a relaxation of the strong Wolfe conditions and it allows to accept larger steps. The proposed conjugate gradient methods are still globally convergent and, at the same time, they should not suffer the propensit...

In this paper the problem is considered of FCM histogram processing in the case of mixtures of two or more cell populations, which appears of great interest in diagnosis and treatment of tumor diseases. A suitable mathematical model is first developed in order to represent the pattern of DNA and fluorescence distribution in the samples. An optimiza...

In this paper we define two classes of algorithms for the solution of constrained problems. The first class is based on a continuously differentiable exact penalty function, with the additional inclusion of a barrier term. The second class is based on a similar modification performed on a continuously differentiable exact augmented Lagrangian funct...

In this paper we define Newton-type algorithms for the solution of box constrained quadratic programming problems. These algorithms are based on the unconstrained minimization of a continuously differentiable exact penalty function and make use of consistent approximations of the Newton's direction of the penalty function. Under suitable assumption...

In this paper we propose a new derivative-free algorithm for linearly constrained finite minimax problems. Due to the nonsmoothness of this class of problems, standard derivative-free algorithms can locate only points which satisfy weak necessary optimality conditions. In this work we define a new derivative-free algorithm which is globally converg...

We define a primal-dual algorithm model (second-order Lagrangian algorithm, SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second-order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the...

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 rela...