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Teoria dell’ottimizzazione e applicazioni

Scuola di dottorato in Teora dell’ottimizzazione e applicazioni,

Ingegneria, Palermo, febbraio-aprile 2011, organizzatori Riva-SanSeverino e Cassará

1° Modulo (4 ore)

  • Numerical Optimization (Cassarà) 23/02 ore 15

* Affine and convex sets

* Convex functions

* Optimization problems

* Convex optimization

* Linear optimization problems

* Quadratic optimization problems

* Geometric programming

* The Lagrange dual function

* The Lagrange dual problem

  • Linear programming (Cassarà) 02/03 ore 15

* Unconstrained minimization

* Equality constrained minimization

* Interior-point methods

2° Modulo (6 ore)

  • Combinatorial Optimization (Cassarà) 09/03 ore 15

* Introduction to combinatorial Optimization

* Combinatorial Optimization Problems (TSP, LPP, Max-Cut, Buffer Allocation)

* The Cross-Entropy Method

  • Stochastic Optimization (Bauso) 16/03 ore 15

* Introduction to Stochastic Programming

* Certainty equivalence

* Chance Constraints

* Connection with Robust Optimization

  • An Introduction to Optimization Heuristic (Riva San Severino) 23/03 ore 15

* Optimization heuristics (an overview)

* Heuristic optimization paradigm

* Overview of optimization heuristics

* Local search: Simulated annealing, Tabu Search (Pseudo-code and main features)

* Population based search: Genetic algorithm, Ant colonies, Glow-worm Swarm

* Optimization (Pseudo-code and main features)

3° Modulo (6 ore)

  • Distributed Optimization (Bauso) 30/03 ore 15

* Dual Decomposition

* Team Theory

* Person-by-Person Optimization

* Linear Quadratic Gaussian Distributed Problems Discrete Action Spaces

* Unimodularity vs. Convexity

* Best-Response Paths and Potential Games

* Graph Theory

* The Consensus Problem

* Distributed consensus protocols for coordinating buyers

* Mechanism Design for Optimal Consensus Problems

* Lazy consensus for networks with unknown but bounded disturbances

  • Evolutionary Algorithms (E.A.) for Multi-Objective Optimization  (M.O.) (Riva San Severino) 13/04 ore 15

* The general M.O. Problem

* Pareto optimality

* Basic definitions for E.A

* Types of M.O.E.A

* Diversification techniques on the P.F.

* Constraints representation

* Power systems optimization problems (Applications)

4° Modulo (4 ore)

  • MATLAB Application (Mangione) 20/04 – 27/04 ore 15

* Introduction to Optimization ToolBox

* Algorithm Implementation Examples

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