Giovanni RUSSO | OPTIMIZATION TECHNIQUES FOR ENGINEERS
Giovanni RUSSO OPTIMIZATION TECHNIQUES FOR ENGINEERS
cod. 8802000004
OPTIMIZATION TECHNIQUES FOR ENGINEERS
| 8802000004 | |
| DIPARTIMENTO DI INGEGNERIA DELL'INFORMAZIONE ED ELETTRICA E MATEMATICA APPLICATA | |
| Corso di Dottorato (D.M.45/2013) | |
| INGEGNERIA DELL'INFORMAZIONE | |
| 2021/2022 |
| OBBLIGATORIO | |
| ANNO CORSO 1 | |
| ANNO ORDINAMENTO 2021 | |
| ANNUALE |
| SSD | CFU | ORE | ATTIVITÀ | |
|---|---|---|---|---|
| MAT/09 | 3 | 18 | LEZIONE |
| Obiettivi | |
|---|---|
| MATHEMATICAL OPTIMIZATION IS CONCERNED WITH FINDING THE BEST AVAILABLE VALUE OF AN OBJECTIVE FUNCTION THROUGH APPROPRIATELY CHOOSING CERTAIN DECISION VARIABLES WITHIN A SET OF GIVEN CONSTRAINTS. A BROAD VARIETY OF PROBLEMS ARISING FROM DIVERSE APPLICATIONS, INCLUDING PRODUCTION OPTIMIZATION, SCHEDULING, RESOURCES ASSIGNMENT, PORTFOLIO MANAGEMENT, CAN ALL BE FORMULATED AS MATHEMATICAL OPTIMIZATION PROBLEMS. THIS MODULE PRESENTS THE MATHEMATICAL CONCEPTS AND ALGORITHMIC TOOLS FOR MODELING AND SOLVING A CLASS OF OPTIMIZATION PROBLEMS EXTREMELY USEFUL IN APPLICATIONS: CONVEX PROBLEMS. KNOWLEDGE AND UNDERSTANDING AT THE OF THE MODULE, STUDENTS WILL BE ABLE TO: • TO FORMULATE REAL WORLD OPTIMIZATION PROBLEMS AND INCORPORATE UNCERTAINTY; • USE DUALITY THEORY TO FIND OPTIMAL SOLUTIONS; • LEVERAGE BASIC RESULTS ON CONVEX OPTIMIZATION TO SOLVE THESE IMPORTANT PROBLEMS. PRACTICAL SKILLS • FORMULATE OPTIMIZATION PROBLEMS STARTING FROM HIGH-LEVEL SPECIFICATIONS; • IMPLEMENT OPTIMIZATION SOLVERS AND USE OFF-THE-SHELF TOOLS; • USE THEORETICAL TOOLS TO CRITICALLY ASSESS THE RESULTS OBTAINED FROM THE SOLVERS. |
| Prerequisiti | |
|---|---|
| THE STUDENT SHOULD BE FAMILIAR WITH MATHEMATICAL ANALYSIS, LINEAR ALGEBRA AND NUMERICAL METHODS. |
| Contenuti | |
|---|---|
| INTRODUCTION: WHAT IS OPTIMIZATION AND POSSIBLE OUTCOMES OF AN OPTIMIZATION PROBLEM. LINEAR PROGRAMMING: EXAMPLES, THE SIMPLEX ALGORITHM AND ITS IMPLEMENTATION, RELATION WITH DUALITY INTEGER PROGRAMMING: EXAMPLES AND SOLUTION ALGORITHMS: BRANCH & BOUND AND CUTTING PLANES CONVEX OPTIMIZATION: CONVEX FUNCTIONS, OPTIMALITY CONDITIONS, QUADRATIC OPTIMIZATION, CONVEX RELAXATIONS OF NON-CONVEX PROBLEMS DUALITY: THE KEY IDEA OF LAGRANGE DUALITY, THE LAGRANGIAN FUNCTION AND HE LAGRANGE DUAL, WEAK & STRONG DUALITY NUMERICAL ALGORITHMS: GRADIENT DESCENT METHODS, QUASI-NEWTON METHODS, INTERIOR-POINT METHODS, SUB-GRADIENTS BASICS OF OPTIMIZATION UNDER UNCERTAINTY: UNCERTAINTY MODELING, SPECIAL CASES OF MINIMAX OPTIMIZATION SEQUENTIAL OPTIMIZATION |
| Metodi Didattici | |
|---|---|
| • LECTURES SUPPORTED BY PROBLEM-SOLVING TUTORIALS WITH PRACTICAL ASPECTS ALSO COVERED DURING LECTURES. • IN ORDER TO PARTICIPATE TO THE FINAL ASSESSMENT AND TO GAIN THE CREDITS CORRESPONDING TO THE MODULE, THE STUDENT MUST HAVE ATTENDED AT LEAST 65% OF THE HOURS OF ASSISTED TEACHING ACTIVITIES. |
| Verifica dell'apprendimento | |
|---|---|
| THE EXAM CONSISTS OF A WRITTEN TEST. THE TEST INCLUDES BOTH METHODOLOGICAL QUESTIONS AND PROBLEMS REQUIRING THE USE OF NUMERICAL METHODS. POSSIBLE GRADES ARE, IN DESCENDING ORDER: OTTIMO (EXCELLENT), BUONO (GOOD), DISCRETE (FAIR), SUFFICIENTE (PASS), INSUFFICIENTE (FAIL). STUDENTS WHO GET AN INSUFFICIENTE (FAIL) MARK OR REJECT THE GIVEN MARK CAN REPEAT THE EXAM ONLY ONCE AFTER AT LEAST 30 DAYS. |
| Testi | |
|---|---|
| • B. GUENIN, J. KONEMANN, L. TUNCEL, A GENTLE INTRODUCTION TO OPTIMIZATION, CAMBRIDGE UNIVERSITY PRESS, 2014. • R. KWON, INTRODUCTION TO LINEAR OPTIMIZATION AND EXTENSIONS WITH MATLAB, CRC PRESS 2014. • S. BOYD, L. VANDENBERGHE, CONVEX OPTIMIZATION, CAMBRIDGE UNIVERSITY PRESS, 2004. |
| Altre Informazioni | |
|---|---|
| COMPULSORY ATTENDANCE. TEACHING LANGUAGE IS ENGLISH. |
BETA VERSION Fonte dati ESSE3 [Ultima Sincronizzazione: 2022-11-21]
