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OP03b-Graident Methods PDF

The document discusses gradient methods for optimization. It covers the gradient method and steepest descent method. It provides references on optimization and discusses concepts like gradients, Hessians, Taylor series, and level sets. Examples are provided on using gradient descent to optimize quadratic functions. Homework is assigned to design a finite impulse response filter using gradient methods.

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59 views22 pages

OP03b-Graident Methods PDF

The document discusses gradient methods for optimization. It covers the gradient method and steepest descent method. It provides references on optimization and discusses concepts like gradients, Hessians, Taylor series, and level sets. Examples are provided on using gradient descent to optimize quadratic functions. Homework is assigned to design a finite impulse response filter using gradient methods.

Uploaded by

tranhieu_hcmut
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Gradient Methods

Lectured by Ha Hoang Kha, Ph.D.


Ho Chi Minh City University of Technology
Email: hahoangkha@gmail.com

Content
Gradient method
The Steepest descent method

References
E. K. P. Chong and S. H. Zak, An Introduction to
Optimization, Jonh Wiley & Sons, 2001.

Gradient and Hessian

Taylor Series

Level set

Gradient Method

Gradient Method

Gradient Descent Method (Gradient Method)

Gradient methods are simple to implement and often


perform well they are widely used in practical
applications.
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Steepest Descent

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Steepest Descent

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Stopping criterion

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Example

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Example

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Example

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Quadratic Function Optimization


Quadratic function

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Quadratic Function Optimization

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Homework: FIR Filter Design

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Homework: FIR Filter Design

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Homework: FIR Filter Design


Design a FIR filter of order N=160

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Homework: FIR Filter Design

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Homework

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