Ph.D. School in Analytics for Economics and Business COURSE: Java, C++ and CPLEX laboratory

Teacher: Enrico Angelelli Reference: Enrico Angelelli Dept. of Economics and Management University of Brescia Univ. tel: 0039 030 2988583 e‐mail(s): [email protected]

Course description and objectives The aim of this course is to introduce technical tools to implement algorithms for the solution of discrete optimization and mixed integer problems. The computational complexity of most of the optimization problems arising in operations management together with the large amount of data usually involved requires the development of ad‐hoc algorithms as general purpose optimization software products often fail to find optimal or even good solutions in a reasonable amount of time. In this course some technical tools will be introduced to approach software development in Java and C++. After an introduction to Object Oriented Programming principles, two object oriented programming languages will be proposed: Java and C++. For both languages an appropriate development environment will be presented and main data structures made available by standard libraries will be introduced. Moreover, in this course we introduce the ILOG Concert Technology library that is one of the two component libraries included in IBM ILOG CPLEX Optimization Studio. ILOG Concert Technology allows one to define mathematical programming models for CPLEX and to customize the solution algorithms. The course is based on assisted lab activities, integrated by personal work, and aims at making the student able to develop a small software project.

Outline a) Getting started with Java: IDE, syntax, variables and arrays, flow control structures, functions, compiling and running a code. b) Object oriented programming paradigm: ideas and examples. c) Object oriented programming in Java: building a project in Netbeans, data structures in Java standard library. d) Implementing data structures in Java. e) ILOG Concert Technology: build and solve a model with standard solver. Concert technology Call‐ backs f) Using Concert Technology in C/C++

References Refence textbooks ‐ Thinking in Java, B. Eckel, Prentice Hall Ptr; 4th edition. ‐ Thinking in C++: Introduction to Standard C++, Volume One, B. Eckel, Prentice Hall; 2 edition (March 25, 2000) ‐ Thinking in C++, Volume 2: Practical Programming, B. Eckel, C. AllisonPrentice Hall; 1 edition (December 27, 2003) Online resources ‐ Java Tutorial ‐ http://www.tutorialspoint.com/java/java_pdf_version.htm ‐ C++ Tutorial ‐ http://www.tutorialspoint.com/cplusplus/cpp_pdf_version.htm More documentation ‐ Online documentation for Concert technology Ph.D. School in Analytics for Economics and Business COURSE: Optimal and heuristic algorithms for NP‐hard problems

Teacher: Claudia Archetti

Reference: Claudia Archetti

Dept. of Economics and Management

University of Brescia

Univ. tel: 0039 030 2988587 e‐mail(s): [email protected]

Course description and objectives

The scope of this course is to present standard schemes for the exact and heuristic solution of combinatorial optimization problems. The objective of the course is to provide the students with the most effective tools that are used to handle combinatorial optimization problems, in particular NP‐hard problems. Practical applications of the solution schemes to different basic problems will be presented.

Outline

1. a Exact algorithms: the standard and most effective schemes used for the solution of mixed integer linear programs will be analyzed: a. Branch-and-bound: basic concepts, strategies of explorations of the tree, determination of bounds. b. Cutting plane: definition of “cut”, separation algorithms. c. Branch-and-cut: strategies that can be used to efficiently combine branch-and-bound with cutting plane. d. and branch-and-price: introduction to the column generation technique and its embedding into a branch-and-bound algorithm. 2. Heuristic algorithms: the focus will be on classical and recent schemes: a. Greedy algorithms: definition of “greedy”, standard scheme. b. Local search: definition of neighborhood and move. c. : the most classical metaheuristic schemes will be introduced: , , genetic algorithms and variable neighborhood search. d. Matheuristic: combining heuristic/metaheuristic schemes with the exact solution of MILP problems. 3. Approximation algorithms: the concept of “approximation scheme” will be introduced and its application to some classical, and basic, combinatorial optimization problems will be analyzed.

References

C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Books on Computer Science, 2000.

F. Glover, G.A. Kochenberger, Handbook of Metaheurtsics, Springer, 2003.

G. Desaulniers, J. Desrosiers, M.M. Solomon, Column Generation, Springer, 2005. Ph.D. School in Analytics for Economics and Business COURSE: Non Linear Optimization

Teacher: Francesca Maggioni

Dept. of Management, Economics and Quantitative Methods

University of Bergamo

Univ. tel: 0039 035 2052649

Mobile: 0039 340 5059292 e‐mail: [email protected]

Course description and objectives

The course carries 4CFU and its primary focus is on numerical methods for nonlinear optimization.

It is structured in several parts dedicated to a) methods for one‐variable Optimization, b) methods for unconstrained optimization in n variables c) Gauss‐Newton method for least‐squares data fitting, d) introduction to Markowitz portfolio theory e) equality constrained problems f) inequality constrained problems g) minimax data‐fitting via inequality constrained optimization and h) portfolio problems involving global optimization.

The course will enable doctoral students to get in‐depth theoretical and practical knowledge of nonlinear optimization algorithms. Such methods can be applied to many practical problems in management and engineering. A description and derivation is given for most of the currently popular algorithms for continuous nonlinear optimization. For each method, important convergence results are outlined and complemented by numerical illustrations to give a flavour to the students of how the methods perform in practice.

Examples and case studies concerning with portfolio selection and with time‐series problems such as fitting trendlines, are presented and discussed.

Exposure to foundation, seminal contributions as well as to current results and software developments will enable the students to link in a consistent and rigorous way state‐of‐the‐art theory and practical approaches in this area.

Outline

a) One‐variable Optimization ‐ Optimality conditions ‐ Numerical methods for one‐variable minimization (Simplex method, Bisection, Secant method, Newton method) ‐ MATLAB implementations b) Unconstrained optimization in n variables ‐ Optimality conditions ‐ Numerical methods and examples ‐ Simplex and univariate search ‐ Steepest descent with perfect and weak line searches ‐ Newton method, quasi‐Newton methods, conjugate gradient methods c) Gauss‐Newton method for least‐squares data fitting d) Introduction to Markowitz portfolio theory ‐ Minimum risk portfolios ‐ Maximum return portfolios ‐ Other portfolio performance functions ‐ Two‐asset portfolios leading to one variable minimization e) Equality constrained problems ‐ Optimality conditions ‐ Numerical methods ‐ , reduced gradients ‐ Sequential unconstrained minimization ‐ Sequential quadratic programming ‐ Examples of portfolio calculations f) Inequality constrained problems ‐ Optimality conditions ‐ Numerical methods ‐ Quadratic programming, reduced gradients ‐ Sequential unconstrained minimization (including barrier functions) ‐ Sequential quadratic programming ‐ Interior point methods ‐ Example of portfolio calculations g) Minimax data‐fitting via inequality constrained optimization h) Portfolio problems involving global optimization

References

‐ Nonlinear Optimization with Financial Applications by Michael Bartholomew‐Biggs, Springer, 261 p., Hardcover ISBN: 1‐4020‐8110‐3 ‐ Numerical Optimization by Jorge Nocedal and Stephen J.Wright, 2nd edition, Springer, ISBN‐10: 0‐387‐30303‐0 ‐ Optimization − Theory and Practice by Wilhelm Forst and Dieter Hoffmam, Springer, ISBN: 978‐ 0‐38778976‐7