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Numerical Optimization and Data Science

Master in Finance and Laurea Magistrale in Mathematics,

A.A. 2023-24

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The course (48 hours, 6 cfu) consists of 2 parts of 24 hours, 3 cfu each:

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• Numerical Optimization, prof. Luca Pavarino,

Tuesday 4 – 6 pm, room B2 (with some exceptions)

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• Data Science, prof. Davide Duma,

Thursday 4 – 6 pm, room B4 (with some exceptions)

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My contacts:

office E32 Math. Dept.,

Phone: 0382 985643

email luca.pavarino@unipv.it,

Webpage: https://sites.google.com/unipv.it/lucafp/home

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Course webpage:

https://sites.google.com/unipv.it/teaching/numerical-optimization

The three pillars of Data Science:

• Linear Algebra
• Statistics
• Optimization

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All three require numerical algorithms in order to compute solutions, answers, decisions

• Numerical Linear Algebra
• Computational Statistics
• Numerical Optimization

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General Optimization Problem:

find x in S (feasible set) such that

Linear Programming (Linear Optimization): f and/or g, g_i are linear

Quadratic Programming (Quadratic Optimization): f is quadratic

Integer Programming:

Stochastic Programming:

Course Program

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• Introduction
• Derivative – free methods: Nelder – Mead
• Newton’s method
• Descent methods (line search)
• Step size selection
• Newton’s direction
• Quasi – Newton’s directions
• Gradient direction
• Conjugate gradient direction
• Trust – Region methods
• Nonlinear Least – Square methods
• Gauss – Newton
• Levenberg - Marquardt
• Applications to

Artificial Neural Networks

Texts for further information:

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J. Nocedal, S. Wright,

Numerical Optimization, Springer, 2006

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M. J. Kochenderfer, T. A. Wheeler,

Algorithms for Optimization, MIT Press, 2019

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