Francesco CARRABS | OPTIMIZATION

cod. 0522200016

OPTIMIZATION

	0522200016
	DIPARTIMENTO DI MATEMATICA
	EQF7
	MATHEMATICS
	2016/2017

PERCORSO COMUNE Cohort 2015/2016

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2010
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	RAFFAELE CERULLI T Curriculum
	FRANCESCO CARRABS Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE OF INTEGER LINEAR PROGRAMMING PROBLEMS, INTRODUCED IN THE OPERATIONS RESEARCH COURSE. THE COURSE AIMS AT SHOWING HOW TO SOLVE LINEAR PROGRAMMING PROBLEMS WITH A HUGE NUMBER OF VARIABLES OR CONSTRAINTS. MIXED LINEAR INTEGER PROGRAMMING PROBLEMS ARE ALSO OBJECT OF THE COURSE THAT AIMS TO DEEPEN THE KNOWLEDGE OF MATHEMATICAL MODELING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND OF EXACT AND APPROXIMATION ALGORITHMS TO SOLVE THEM. APPLYING KNOWLEDGE AND UNDERSTANDING: ABILITY TO RECOGNIZE AND TO FORMULATE LINEAR OPTIMIZATION PROBLEMS AND MIXED INTEGER LINEAR OPTIMIZATION PROBLEMS. KNOWLEDGE OF THE MATHEMATICAL PROPERTIES OF THE PROBLEMS AND OF THEIR INHERENT COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE MOST RECENT AND EFFICIENT ALGORITHMS FOR THE EXACT SOLUTION OF THE PROBLEMS OF PLI. KNOWLEDGE OF THE MAIN ELEMENTS FOR SOLVING LARGE PROBLEMS: CALCULATION OF LOWER BOUND AND DESIGN OF HEURISTIC ALGORITHMS.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE OF INTEGER LINEAR PROGRAMMING PROBLEMS, INTRODUCED IN THE OPERATIONS RESEARCH COURSE. THE COURSE AIMS AT SHOWING HOW TO SOLVE LINEAR PROGRAMMING PROBLEMS WITH A HUGE NUMBER OF VARIABLES OR CONSTRAINTS. MIXED LINEAR INTEGER PROGRAMMING PROBLEMS ARE ALSO OBJECT OF THE COURSE THAT AIMS TO DEEPEN THE KNOWLEDGE OF
MATHEMATICAL MODELING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND OF EXACT AND APPROXIMATION ALGORITHMS TO SOLVE THEM.

APPLYING KNOWLEDGE AND UNDERSTANDING:
ABILITY TO RECOGNIZE AND TO FORMULATE LINEAR OPTIMIZATION PROBLEMS AND MIXED INTEGER LINEAR OPTIMIZATION PROBLEMS. KNOWLEDGE OF THE MATHEMATICAL PROPERTIES OF THE PROBLEMS AND OF THEIR INHERENT COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE MOST RECENT AND EFFICIENT ALGORITHMS FOR THE EXACT SOLUTION OF THE PROBLEMS OF PLI. KNOWLEDGE OF THE MAIN ELEMENTS FOR SOLVING LARGE PROBLEMS: CALCULATION OF LOWER BOUND AND DESIGN OF HEURISTIC ALGORITHMS.

	Prerequisites
	STUDENTS SHOULD KNOW BASIC CONCEPTS OF OPERATIONS RESEARCH.

	Contents
	MATHEMATICAL PROGRAMMING AND OPTIMALITY CONDITIONS. DUALITY THEORY. MAIN ELEMENTS OF THE ELLIPSOID METHOD. DUAL SIMPLEX. SOLUTION ALGORITHMS FOR LARGE SIZE PROBLEMS: COLUMN GENERATION METHOD. PRIMAL-DUAL METHOD. DISCRETE OPTIMIZATION: NETWORK FLOW PROBLEMS. MAIN CLASSES OF COMBINATORIAL PROBLEMS. VALID INEQUALITIES. RELAXATIONS. BENDERS DECOMPOSITION. EXACT SOLUTION METHODS: BRANCH AND BOUND, BRANCH AND CUT, CUTTING PLANE, BRANCH AND PRICE. LOCAL SEARCH ALGORITHMS AND METAHEURISTICS.

Contents

MATHEMATICAL PROGRAMMING AND OPTIMALITY CONDITIONS. DUALITY THEORY. MAIN ELEMENTS OF THE
ELLIPSOID METHOD. DUAL SIMPLEX. SOLUTION ALGORITHMS FOR LARGE SIZE PROBLEMS: COLUMN GENERATION METHOD. PRIMAL-DUAL METHOD.
DISCRETE OPTIMIZATION: NETWORK FLOW PROBLEMS. MAIN CLASSES OF COMBINATORIAL PROBLEMS. VALID
INEQUALITIES. RELAXATIONS. BENDERS DECOMPOSITION. EXACT SOLUTION METHODS: BRANCH AND BOUND,
BRANCH AND CUT, CUTTING PLANE, BRANCH AND PRICE. LOCAL SEARCH ALGORITHMS AND METAHEURISTICS.

	Teaching Methods
	TRADITIONAL LESSONS.

	Verification of learning
	ORAL EXAMINATION.

	Texts
	LECTURE NOTES.

	More Information
	EMAILS: FCARRABS@UNISA.IT RAFFAELE@UNISA.IT SITE1 : WWW.DIPMAT.UNISA.IT/PEOPLE/CARRABS/WWW/ WWW.DIPMAT.UNISA.IT/PEOPLE/CERULLI/WWW

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Francesco CARRABS | OPTIMIZATION