Gianni Di Pillo | Università degli Studi "La Sapienza" di Roma (original) (raw)

Papers by Gianni Di Pillo

Research paper thumbnail of A DIRECT-type approach for derivative-free constrained global optimization

Computational Optimization and Applications, 2016

In the field of global optimization, many efforts have been devoted to globally solving bound con... more 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 with a derivative-free local minimization of a nonsmooth exact penalty function. In particular, we define a new DIRECT-type strategy to explore the search space by explicitly taking into account the twofold nature of the optimization problems, i.e. the global optimization of both the objective function and of a feasibility measure. We report an extensive experimentation on hard test problems to show viability of the approach.

Research paper thumbnail of Universitta degli Studi di Roma? La Sapien

Research paper thumbnail of An algorithm for the nonlinear programming problem of the railway Yield Management

Research paper thumbnail of Nonlinear programming

Research paper thumbnail of Fruitful uses of smooth exact merit functions in constrained optimization

Applied Optimization, 2003

Research paper thumbnail of An exact penalty-Lagrangian approach for large-scale nonlinear programming

Research paper thumbnail of Use of a truncated Newton direction in an augmented Lagrangian framework

Use of a truncated Newton direction in an augmented Lagrangian framework Gianni Di Pillo (dipillo... more Use of a truncated Newton direction in an augmented Lagrangian framework Gianni Di Pillo (dipillo@dis.uniromal.it) Giampaolo Liuzzi1 (liuzzi@dis.uniromal.it) Stefano ... into a horizontal stepi d0 in the null space N(ygAk{xk)') and a vertical step dv in the range space TZ(\7gAk(xk ...

Research paper thumbnail of An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information

Journal of Optimization Theory and Applications, 2022

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints an... more 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 incorporate second-order information into the augmented Lagrangian framework, using an active-set strategy. We show that the overall algorithm has the same convergence properties as ALGENCAN and an asymptotic quadratic convergence rate under suitable assumptions. The numerical results confirm that the proposed algorithm is a viable alternative to ALGENCAN with greater robustness.

Research paper thumbnail of Algorithms for Continuous Optimization: The State of Art NATO Advanced Study Institute, I1 Ciocco, Barga, Italy, 5-18 September 1993

Research paper thumbnail of An exact augmented Lagrangian function exploiting negative curvature directions

In this paper we propose a primal-dual algorithm for the solution of inequality constrained optim... more In this paper 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. In the unconstrained case this task is accomplished by computing a suitable negative curvature direction of the objective function. In the constrained case it is possible to gain analogous information by exploiting the non-convexity of a particular exact merit function. The algorithm employes an adaptive linesearch procedure whose distinguishing feature is that of comparing, at every iteration, the relative effects of two directions and then selecting the more promising one. The first direction conveys first order information on the problem and can be used to define a sequence of points converging toward a KKT pair of the problem. Whereas, the second direction conveys information on the local non-convexity of the problem and can be used ...

Research paper thumbnail of A Shifted-Barrier Primal-Dual Algorithm Model for Linearly Constrained Optimization Problems

Computational Optimization, 1999

In this paper we describe a Newton-type algorithm model for solving smooth constrained optimizati... more In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs {x k , λ k } converging quadratically to a pair (x,λ) wherex satisfies the first order necessary conditions andλ is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence {x k } alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported.

Research paper thumbnail of A primal-dual algorithm for nonlinear programming exploiting negative curvature directions

Numerical Algebra, Control & Optimization, 2011

... Gianni Di Pillo∗, Giampaolo Liuzzi†, Stefano Lucidi∗ ... Let K ⊆ {1,...,p} be an index subset... more ... Gianni Di Pillo∗, Giampaolo Liuzzi†, Stefano Lucidi∗ ... Let K ⊆ {1,...,p} be an index subset, we denote by vK the subvector of v with components vi such that i ∈ K. Given two vectors v, w ∈ IRp, the operation max{v, w} is intended component-wise, namely max{v, w} denotes the ...

Research paper thumbnail of On Exact Augmented Lagrangian Functions in Nonlinear Programming

Nonlinear Optimization and Applications, 1996

This paper is our modest tribute to Elijah Polak, an eminent scholar who greatly influenced the d... more This paper is our modest tribute to Elijah Polak, an eminent scholar who greatly influenced the development of optimization theory and practice for over forty years. Several of his contributions in unconstrained and constrained nonlinear programming, both in the smooth and in the non smooth case, in the analysis and optimization of control systems, in the implementation of effective design methods in engineering, are milestones. We are in particular grateful to Eljiah for his work on exact penalty algorithms, from which we derived much inspiration, including some at the basis of this paper.

Research paper thumbnail of An application of learning machines to sales forecasting under promotions

This paper deals with sales forecasting in retail stores of large distribution. For several years... more This paper deals with sales forecasting in retail stores of large distribution. For several 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 in case of promotions, because they are not well suited to model the nonlinear behaviors of the sales process. In the last years new methods based on Learning Machines are being employed for forecasting problems. These methods realize universal approximators of non linear functions, thus resulting more able to model complex nonlinear phenomena. The paper proposes an assessment of the use of Learning Machines for sales forecasting under promotions, and a comparison with the statistical methods, making reference to two real world cases. The learning machines have been trained using several configuration of input attributes, to point out the importance of a suitable inputs selection.

Research paper thumbnail of An application of support vector machines to sales forecasting under promotions

4OR, 2016

This paper deals with sales forecasting of a given commodity in a retail store of large distribut... more 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 are not well suited to model the nonlinear behaviors of the sales process. In recent years new methods based on machine learning are being employed for forecasting applications. A preliminary investigation indicates that methods based on the support vector machine (SVM) are more promising than other machine learning methods for the case considered. The paper assesses the application of SVM to sales forecasting under promotion impacts, compares SVM with other statistical methods, and tackles two real case studies.

Research paper thumbnail of High Performance Algorithms and Software for Nonlinear Optimization

Applied Optimization, 2003

Softcover reprint of the hardcover I st edition 2003 All righ1s reserved. No part ofthis publicat... more Softcover reprint of the hardcover I st edition 2003 All righ1s reserved. No part ofthis publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying , microfihning, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Research paper thumbnail of A superlinearly convergent primal — dual algorithm model for constrained optimization problems with bounded variables

Optimization Methods and Software, 2000

Research paper thumbnail of An exact penalty-lagrangian approach for a class of constrained optimization problems with bounded variables

Optimization, 1993

In this paper we consider a class of equality constrained optimization problems with box constrai... more In this paper we consider a class of equality constrained optimization problems with box constraints on a part of its variablesThe study of non linear programming problems with such a structure is justified by the existence of practical problems in many fields as, for example, optimal control or economic modelling. Typically, the dimension of these problems are very large and,

Research paper thumbnail of Optimal Location of a Measurement Point in a Diffusion Process

Research paper thumbnail of Identification of distributed-parameter systems with missing data}

Proceedings of the 2012 American Control Conference}, 2012

Bibtex entries of all publications. Bart De Schutter. @techreport{HidDeS:12-023, author={Z. Hiday... more Bibtex entries of all publications. Bart De Schutter. @techreport{HidDeS:12-023, author={Z. Hidayat and A. N{\'{u}}{\~n}}ez and R. Babu{\v{s}}ka and B. {D}e Schutter}, title={Identification of distributed-parameter systems with missing data}, number={12-023}, institution={Delft Center for Systems and Control, Delft University of Technology}, address={Delft, The Netherlands}, month=jun, year={2012}, note={Accepted for the \emph{2012 IEEE International ...

Research paper thumbnail of A DIRECT-type approach for derivative-free constrained global optimization

Computational Optimization and Applications, 2016

In the field of global optimization, many efforts have been devoted to globally solving bound con... more 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 with a derivative-free local minimization of a nonsmooth exact penalty function. In particular, we define a new DIRECT-type strategy to explore the search space by explicitly taking into account the twofold nature of the optimization problems, i.e. the global optimization of both the objective function and of a feasibility measure. We report an extensive experimentation on hard test problems to show viability of the approach.

Research paper thumbnail of Universitta degli Studi di Roma? La Sapien

Research paper thumbnail of An algorithm for the nonlinear programming problem of the railway Yield Management

Research paper thumbnail of Nonlinear programming

Research paper thumbnail of Fruitful uses of smooth exact merit functions in constrained optimization

Applied Optimization, 2003

Research paper thumbnail of An exact penalty-Lagrangian approach for large-scale nonlinear programming

Research paper thumbnail of Use of a truncated Newton direction in an augmented Lagrangian framework

Use of a truncated Newton direction in an augmented Lagrangian framework Gianni Di Pillo (dipillo... more Use of a truncated Newton direction in an augmented Lagrangian framework Gianni Di Pillo (dipillo@dis.uniromal.it) Giampaolo Liuzzi1 (liuzzi@dis.uniromal.it) Stefano ... into a horizontal stepi d0 in the null space N(ygAk{xk)') and a vertical step dv in the range space TZ(\7gAk(xk ...

Research paper thumbnail of An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information

Journal of Optimization Theory and Applications, 2022

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints an... more 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 incorporate second-order information into the augmented Lagrangian framework, using an active-set strategy. We show that the overall algorithm has the same convergence properties as ALGENCAN and an asymptotic quadratic convergence rate under suitable assumptions. The numerical results confirm that the proposed algorithm is a viable alternative to ALGENCAN with greater robustness.

Research paper thumbnail of Algorithms for Continuous Optimization: The State of Art NATO Advanced Study Institute, I1 Ciocco, Barga, Italy, 5-18 September 1993

Research paper thumbnail of An exact augmented Lagrangian function exploiting negative curvature directions

In this paper we propose a primal-dual algorithm for the solution of inequality constrained optim... more In this paper 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. In the unconstrained case this task is accomplished by computing a suitable negative curvature direction of the objective function. In the constrained case it is possible to gain analogous information by exploiting the non-convexity of a particular exact merit function. The algorithm employes an adaptive linesearch procedure whose distinguishing feature is that of comparing, at every iteration, the relative effects of two directions and then selecting the more promising one. The first direction conveys first order information on the problem and can be used to define a sequence of points converging toward a KKT pair of the problem. Whereas, the second direction conveys information on the local non-convexity of the problem and can be used ...

Research paper thumbnail of A Shifted-Barrier Primal-Dual Algorithm Model for Linearly Constrained Optimization Problems

Computational Optimization, 1999

In this paper we describe a Newton-type algorithm model for solving smooth constrained optimizati... more In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs {x k , λ k } converging quadratically to a pair (x,λ) wherex satisfies the first order necessary conditions andλ is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence {x k } alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported.

Research paper thumbnail of A primal-dual algorithm for nonlinear programming exploiting negative curvature directions

Numerical Algebra, Control & Optimization, 2011

... Gianni Di Pillo∗, Giampaolo Liuzzi†, Stefano Lucidi∗ ... Let K ⊆ {1,...,p} be an index subset... more ... Gianni Di Pillo∗, Giampaolo Liuzzi†, Stefano Lucidi∗ ... Let K ⊆ {1,...,p} be an index subset, we denote by vK the subvector of v with components vi such that i ∈ K. Given two vectors v, w ∈ IRp, the operation max{v, w} is intended component-wise, namely max{v, w} denotes the ...

Research paper thumbnail of On Exact Augmented Lagrangian Functions in Nonlinear Programming

Nonlinear Optimization and Applications, 1996

This paper is our modest tribute to Elijah Polak, an eminent scholar who greatly influenced the d... more This paper is our modest tribute to Elijah Polak, an eminent scholar who greatly influenced the development of optimization theory and practice for over forty years. Several of his contributions in unconstrained and constrained nonlinear programming, both in the smooth and in the non smooth case, in the analysis and optimization of control systems, in the implementation of effective design methods in engineering, are milestones. We are in particular grateful to Eljiah for his work on exact penalty algorithms, from which we derived much inspiration, including some at the basis of this paper.

Research paper thumbnail of An application of learning machines to sales forecasting under promotions

This paper deals with sales forecasting in retail stores of large distribution. For several years... more This paper deals with sales forecasting in retail stores of large distribution. For several 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 in case of promotions, because they are not well suited to model the nonlinear behaviors of the sales process. In the last years new methods based on Learning Machines are being employed for forecasting problems. These methods realize universal approximators of non linear functions, thus resulting more able to model complex nonlinear phenomena. The paper proposes an assessment of the use of Learning Machines for sales forecasting under promotions, and a comparison with the statistical methods, making reference to two real world cases. The learning machines have been trained using several configuration of input attributes, to point out the importance of a suitable inputs selection.

Research paper thumbnail of An application of support vector machines to sales forecasting under promotions

4OR, 2016

This paper deals with sales forecasting of a given commodity in a retail store of large distribut... more 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 are not well suited to model the nonlinear behaviors of the sales process. In recent years new methods based on machine learning are being employed for forecasting applications. A preliminary investigation indicates that methods based on the support vector machine (SVM) are more promising than other machine learning methods for the case considered. The paper assesses the application of SVM to sales forecasting under promotion impacts, compares SVM with other statistical methods, and tackles two real case studies.

Research paper thumbnail of High Performance Algorithms and Software for Nonlinear Optimization

Applied Optimization, 2003

Softcover reprint of the hardcover I st edition 2003 All righ1s reserved. No part ofthis publicat... more Softcover reprint of the hardcover I st edition 2003 All righ1s reserved. No part ofthis publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying , microfihning, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Research paper thumbnail of A superlinearly convergent primal — dual algorithm model for constrained optimization problems with bounded variables

Optimization Methods and Software, 2000

Research paper thumbnail of An exact penalty-lagrangian approach for a class of constrained optimization problems with bounded variables

Optimization, 1993

In this paper we consider a class of equality constrained optimization problems with box constrai... more In this paper we consider a class of equality constrained optimization problems with box constraints on a part of its variablesThe study of non linear programming problems with such a structure is justified by the existence of practical problems in many fields as, for example, optimal control or economic modelling. Typically, the dimension of these problems are very large and,

Research paper thumbnail of Optimal Location of a Measurement Point in a Diffusion Process

Research paper thumbnail of Identification of distributed-parameter systems with missing data}

Proceedings of the 2012 American Control Conference}, 2012

Bibtex entries of all publications. Bart De Schutter. @techreport{HidDeS:12-023, author={Z. Hiday... more Bibtex entries of all publications. Bart De Schutter. @techreport{HidDeS:12-023, author={Z. Hidayat and A. N{\'{u}}{\~n}}ez and R. Babu{\v{s}}ka and B. {D}e Schutter}, title={Identification of distributed-parameter systems with missing data}, number={12-023}, institution={Delft Center for Systems and Control, Delft University of Technology}, address={Delft, The Netherlands}, month=jun, year={2012}, note={Accepted for the \emph{2012 IEEE International ...