Lectured by Ha Hoang Kha, Ph.D.

Ho Chi Minh City University of Technology

Email: hahoangkha@gmail.com

Unconstrained Optimization

Introduction

Conditions for local minimizers

Content

2

References

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

3

Optimization Problem

4

Preliminary

5

Example

6

Feasible direction

7

Directional derivative

8

Example

9

First-order necessary condition (FONC)

10

First-order necessary condition (FONC)

11

First-order necessary condition (FONC)

(Cont.)

12

Example

13

Example

14

Example

15

Second-order necessary condition (SONC)

16

Example

17

Example

18

Second-order sufficient condition (SOSC)

19

Example

20