Contents

Convex sets and Convex functions. 

Unconstrained minimization: Optimality conditions. Generic minimization scheme. Descent methods, Gradient descent method, Newton’s method, Quasi-Newton’s method.

 
Constrained Programming: Lagrange dual function, Optimality conditions, Equality constrained minimization problems, Sequential quadratic programming


Objectives

D1.1 Know optimality conditions for unconstrained optimization
D1.2 Know optimality conditions for constrained optimization. 
D1.3 Illustrate the main features of algorithms for unconstrained, equality

        constrained and inequality constrained optimization problems 
D2.1 Classify and compare various models and algorithms for nonlinear

        optimization problems 
D2.2 Utilize specific software for solving nonlinear optimization problems
D3.1 Choose between different algorithms the most suited for solving specific

        nonlinear optimization problems

D3.2 Evaluate advantages and disadvantages of individual algorithms for nonlinear optimization
D4.1 Discuss the main aspects (theoretical and algorithmc) in nonlinear optimization
D5.1 Deepen through personal study, the most recent aspects of Nonlinear Programming
D5.2 Study independently the most recent algorithmic developments in the area.

Prerequisites

Elements of Operations Research,
Models and algorithms for Linear Programming problems.


Textbooks

 

Renato De Leone Lecture Notes, 2014
Stephen Boyd, Lieven Vandenberghe.
Convex Optimization, Cambridge University Press, 2004
Luigi Grippo, Mario Sciandrone , Metodi di ottimizzazione non vincolata , Springer Unitext 2011

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