# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2016/2017
Belonging course:
Course of Master's Degree Programme on METODI QUANTITATIVI PER LE DECISIONI AZIENDALI
Location:
Napoli
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Credits:
6
Year of study:
1
Teachers:
Cycle:
Second semester
Hours of front activity:
48

### Course description

Through the analysis of some business problems , using methods and mathematical models , the calculation procedures are discussed that may be of help for the identification of the optimal operational
KNOWLEDGE AND CAPACITY OF COMPRESSION: The student must demonstrate to understand the differential calculus related to differential equations to apply them to the study of the Calculus of Variations
CAPACITY TO APPLY KNOWLEDGE AND CAPACITY OF COMPRESSION The student must demonstrate how to apply the knowledge of the differential equations acquired to solve optimization problems. For this purpose, the teacher during the course for the attendants and at the reception for non-attendants provides several exercises.he student must demonstrate knowing how to apply the knowledge of differential and integral calculus acquired to solve optimization problems. For this purpose, the teacher during the course for the attendants and at the reception for non-attendants provides several exercises.
JUDGMENT AUTONOMY: The student must demonstrate the ability to further study independently, acquired knowledge by applying them also through self-evaluation
COMMUCATIVE SKILLS: The student must be able to answer clearly, concisely and exhaustively both in the written test questions and in the oral test.
LEARNING ABILITY: The student must demonstrate a good learning ability by deepening their knowledge on relevant bibliographic references relevant to the field of study.

### Prerequisites

Integral and differential Calculus

### Syllabus

I module: (12 hours)
INTRODUCTION TO THE OPTIMAL CONTROL
Some introductory problems The problem of lunar landing, the foundation of Carthage and the extraction of a finite resource, a production problem and consumption, the construction of roads in the mountains.
II module (12 hours):
Formulation of an optimal control problem Definition of controls, dynamic, trajectories, together with the control. Controls eligible and within regions. Importance of the case of linear dynamics.
III module (12 ore): The OPTIMAL CONTROL METHOD WITH VARIATIONAL The simplest problem of optimal control theorem of Pontryagin comments, and the consequences of the maximum principle. extremal control, associated multiplier. Normal and Abnormal control. Sufficient optimality conditions: the condition of Mangasarian and the condition of Arrow. conditions for problems with starting / ending points set. On minimum problems.
IV module (12 hours)
Production model and inventory management I.The simplest problem of the calculus of variations Euler's theorem; the Euler equation in special cases. conditions for problems with starting / ending points set. sufficient conditions for the simpler problem using concave / convex. minimum length curve.Controls singular and bang-bang-bang-bang of definitions controls, switching instants and unique controls. The construction of a mountain road at minimal cost. more general problem of optimal control of Mayer Problems, Bolza and Lagrange: their equivalence. A necessary condition for the final time Bolza problem with fixed or free. Bolza problems in the calculation of variations: the necessary and sufficient conditions. The adjustment model of labor demand (Hamermesh).

### Textbooks

L.C.s Evans "An introduction to mathematical optimal control theory",
Notes distributed during class

### Learning assessment

The assessment is based on a structured written test in order to evaluate the student's achievement of the learning objectives. An oral test will be conducted to evaluate the acquisition and depth of learning of general theoretical knowledge.