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Algorithms For Constrained Optimization


Veronica Piccialli
Università di Roma Tor Vergata
Course Type
Type A
May 22-26 2017

May 22 14:00-18:00 Room 149
May 23 09:00-13:00 Room 401
May 24 09:00-13:00 Room 143
May 25 09:00-13:00 Room 143
May 26 09:00-13:00 Room 143

1. 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. Karush-Kuhn-Tucker conditions
    Unconstrained Optimization Algorithms: exact line search, Armijo line search. Gradient method.

2. Algorithms for Constrained Optimization Problems with convex feasible set
        Frank wolfe method
        Projected gradient method

3. Algorithms for Constrained Optimization with general constraints
        Sequential penalty method
        Augmented Lagrangian
        Exact penalty functions
        Exact Augmented Lagrangian

4. Quadratic Programming
        Wolfe duality theory
        An application: training of a  Support Vector Machine (SVM)
        Hints on decomposition methods for SVM



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