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Algorithms For Constrained Optimization


Veronica Piccialli
Università di Roma Tor Vergata
Course Type
Type A
September 23 h. 14:00-18:00 Aula 20
September 24 h. 9:00-13:00 Aula 20
September 25 h. 9:00-13:00 Laboratorio Metodi Decisionali ( r104-r105)
September 26 h. 9:00-13:00 Laboratorio Metodi Decisionali ( r104-r105)
September 27 h. 9:00-13:00 Laboratorio Metodi Decisionali ( r104-r105)
Mathematical Programming models: introduction and first definitions
Convex Programming (no local non global minima)
Optimality conditions for unconstrained optimization and constrained optimization. Special cases: convex feasible set, linear constraints, box constraints. Krush-Kuhn-Tucker conditions
Unconstrained Optimization Algorithms: exact line search, Armijo line search. Gradient method.
Algorithms for Constrained Optimization Problems with convex feasible set:
-- Frank Wolfe method
-- Projected gradient method
Algorithms for Constrained Optimization with general constraints:
-- Sequential penalty method
-- Augmented Lagrangian
-- Exact penalty functions
-- Exact Augmented Lagrangian
Quadratic Programming:
-- Wolfe duality theory
-- An application: training of a Support Vector Machine (SVM)
-- Hints on decomposition methods for SVM



PhD Students/Alumni

Dip. Ingegneria dell'Informazione e Scienze Matematiche - Via Roma, 56 53100 SIENA - Italy