Lecture 15 | Convex Optimization I (Stanford)

Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on how unconstrained minimization can be used in electrical engineering and convex optimization for the course, Convex Optimization I (EE 364A).
Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Complete Playlist for the Course:
czcams.com/users/view_play_list...
EE 364A Course Website:
www.stanford.edu/class/ee364
Stanford University:
www.stanford.edu/
Stanford University Channel on CZcams:
/ stanford

[@shiv093]

2:11 Unconstrained minimization
4:00 Initial point and sublevel set
8:15 (10:15) Strong convexity and implications
13:45 Descent methods
16:46 Line search types
23:56 Gradient descent method
26:40 quadratic problem in R^2
29:26 nonquadratic example
29:42 a problem in R^100
32:03 Steepest descent method
34:23 examples
37:50 choice of norm for steepest descent
43:52 Newton step
48:31 Newton decrement
49:51 Newton's method
57:21 Classical convergence analysis
1:02:58 damped newton phase
1:04:51 conclusion
1:09:03 examples in R^2
1:10:42 example in R^10000

[@mrweisu]

The most beneficial lecture in the whole series so far! Super great!

[@divyabhatia9916]

Dr. Boyd, You are just so amazing , funny, super intelligent and down to earth. Thanks so much for making these lectures open source. I learnt a lot from these. Thanks so-3 very much.

[@JaydeepDe]

Beautifully explained the concept of steepest decent for other norms..Thank you professor.

[@TheProgrammer10]

very nice, this course never fails to intimidate me, but makes sense with time

[@heizilyu]

The point that if a constraint is never active the problem is treated as unconstrained (07:54) is excellent!

[@michaelmellinger2324]

39:03 Want the norm to be consistent with the geometry of your sub level sets

[@junhochoi156]

so impressed

[@smolboii1183]

great lecture :d

[@muratcan__22]

perfect

[@luiswilbert2377]

Genius

[@saeedbonab4246]

32:09 should it be argmax instead of argmin?

[@peiqiwang9284]

argmin

[@minseoksong1383]

we're looking for maximum direction to -
abla f(x) in that norm so it should be min for the direction to
abla f(x)

[@jingXD1228]

Most hilarious prof ever

[@toddflanagan5531]

Ch. 9

[@annawilson3824]

1:03:00

[@swagatopablo]

Even Stanford guys copy codes from the web?

[@hotamohit]

yup, but then fail the course if they get caught

[@meetsaiya5007]

Everyone does. But the profs usually knows about these. So the questions are set in such a way you still can't do it. Remember the take home end exam announced in 1st lec, that's basically prof taunting, lets see what you can do. Have been victims of those xD